| Displaying 1-10 of 10 results found.
page
1
0, 3, 0, 6, 0, 6, 6, 12, 6
0, 0, 1, 1, 3, 3, 5, 7, 11, 13
0, 0, 2, 2, 6, 6, 10, 14, 22, 26
Number of triangles in the Y-toothpick structure after n rounds.
+10
5
0, 0, 0, 0, 6, 6, 12, 12, 24, 30
Number of concave-convex hexagons in the Y-toothpick structure of A160120 after n rounds.
+10
5
0, 0, 0, 0, 3, 3, 3, 3, 9, 15
Total number of polygons after n-th stage in the D-toothpick structure of A194270.
+10
4
0, 0, 0, 0, 2, 8, 14, 16, 26, 38, 46, 48, 56, 72, 102
COMMENTS
The structure of the D-toothpick cellular automaton contains at least several tens of different types of polygons. For more information see A194276 and A194277.
EXAMPLE
Consider the structure with toothpicks of length 2 and D-toothpicks of length sqrt(2). After 3 stages the number of polygons in the structure is equal to 0. After 4 stages there are 2 hexagons, each with area = 6, so a(4) = 2. After 5 stages there are new 6 polygons: 2 hexagons, each with area = 8 and also 2 octagons, each with area = 14, so a(5) = 2+6 = 8.
5, 7, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 31, 32, 33, 34, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98
COMMENTS
The asymptotic density of this sequence is 1 (Cooper and Kennedy, 1989). - Amiram Eldar, Jul 10 2020
Triangle read by rows in which row n lists the divisors of n, the n-th prime and the consecutive composites that are greater than the n-th prime, with a(0)=1.
+10
2
1, 1, 2, 1, 2, 3, 4, 1, 3, 5, 6, 1, 2, 4, 7, 8, 9, 10, 1, 5, 11, 12, 1, 2, 3, 6, 13, 14, 15, 16, 1, 7, 17, 18, 1, 2, 4, 8, 19, 20, 21, 22, 1, 3, 9, 23, 24, 25, 26, 27, 28, 1, 2, 5, 10, 29, 30, 1, 11, 31, 32, 33, 34, 35, 36, 1, 2, 3, 4, 6, 12, 37, 38, 39, 40
EXAMPLE
Triangle begins:
1;
1,(2);
1,.2,(3),4;
1,....3,...(5),6;
1,.2,....4,......(7),8,.9,10;
1,..........5,..............(11),12;
1,.2,.3,.......6,..................(13),14,15,16;
1,................7,............................(17),18;
1,.2,....4,..........8,................................(19),20,21,22;
CROSSREFS
Cf. A000005, A000040, A000720, A027750, A018253, A160811, A160812, A161205, A161344, A161345, A161424, A006446, A161827, A161828, A161835.
0, 1, 3, 3, 7, 8, 14, 16, 16, 19, 29, 30, 42, 47, 49, 49, 65, 68, 86, 87, 91, 100, 122, 124, 124, 135, 141, 144, 172, 173, 203, 207, 215, 230, 232, 232, 268, 285, 295, 298, 338, 339, 381, 388, 392, 413, 459, 461, 461, 466, 480, 489, 541, 544, 550, 551, 567, 594
CROSSREFS
Cf. A056737, A018253, A160811, A160812, A161205, A161344, A161345, A161424, A006446, A161828, A161835, A219729, A219730.
Triangle read by rows in which row n lists the divisors of n, prime(n), the consecutive composites that are greater than prime(n), and prime (n+1), but row 0 is formed by 1 and 2.
+10
0
1, 2, 1, 2, 3, 1, 2, 3, 4, 5, 1, 3, 5, 6, 7, 1, 2, 4, 7, 8, 9, 10, 11, 1, 5, 11, 12, 13, 1, 2, 3, 6, 13, 14, 15, 16, 17, 1, 7, 17, 18, 19, 1, 2, 4, 8, 19, 20, 21, 22, 23, 1, 3, 9, 23, 24, 25, 26, 27, 28, 29, 1, 2, 5, 10, 29, 30, 31
COMMENTS
See also A162190, a sequence with a similar structure.
EXAMPLE
Triangle begins:
1,(2);
1,(2),(3);
1,.2.,(3),4,(5);
1,.....3,...(5),6,(7);
1,.2,.....4,......(7),8,.9,10,(11);
1,...........5,...............(11),12,(13);
1,.2,..3,.......6,....................(13),14,15,16,(17);
1,.................7,...............................(17),18,(19);
1,.2,.....4,..........8,....................................(19),20,21,22,(23);
CROSSREFS
Cf. A000005, A000040, A000720, A027750, A018253, A160811, A160812, A161205, A161344, A161345, A161424, A006446, A161827, A161828, A161835, A162190.
Search completed in 0.005 seconds
|