OFFSET
1,2
COMMENTS
The rows of the array can be seen to have the form A(n, k) = p(n)*Fibonacci(k) + q(n)*Fibonacci(k+1) where p(n) is the sequence {0, 1, 3, 3, 3, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, ...}_{n >= 1} and q(n) is the sequence {1, 3, 3, 7, 2, 9, 9, 13, 13, 17, 17, 19, 19, 23, 23, 25, ...}_{n >= 1}. - G. C. Greubel, Jun 23 2022
LINKS
Clark Kimberling, The first column of an interspersion, Fibonacci Quarterly 32 (1994), pp. 301-314.
FORMULA
From G. C. Greubel, Jun 23 2022: (Start)
T(n, 1) = A000045(n+1).
T(n, 2) = A000032(n+1), n >= 2.
T(n, 4) = A022120(n-2), n >= 4.
T(n, 5) = A013655(n-1), n >= 5.
T(n, 6) = A000285(n-2), n >= 6.
T(n, 7) = A022113(n-4), n >= 7.
T(n, 8) = A022096(n-4), n >= 8.
T(n, 9) = A022130(n-6), n >= 9.
T(n, 10) = A022098(n-5), n >= 10.
T(n, 11) = A022095(n-7), n >= 11.
T(n, 12) = A022121(n-8), n >= 12.
T(n, 13) = A022388(n-10), n >= 13.
T(n, 14) = A022122(n-10), n >= 14.
T(n, 15) = A022097(n-10), n >= 15.
T(n, 16) = A022088(n-10), n >= 16.
T(n, 17) = A022390(n-14), n >= 17.
T(n, n) = A199536(n).
T(n, n-1) = A199537(n-1), n >= 2. (End)
EXAMPLE
The even first column stolarsky array (EFC array), northwest corner:
1......2.....3.....5.....8....13....21....34....55....89...144 ... A000045;
4......7....11....18....29....47....76...123...199...322...521 ... A000032;
6......9....15....24....39....63...102...165...267...432...699 ... A022086;
10....17....27....44....71...115...186...301...487...788..1275 ... A022120;
12....19....31....50....81...131...212...343...555...898..1453 ... A013655;
14....23....37....60....97...157...254...411...665..1076..1741 ... A000285;
16....25....41....66...107...173...280...453...733..1186..1919 ... A022113;
20....33....53....86...139...225...364...589...953..1542..2495 ... A022096;
22....35....57....92...149...241...390...631..1021..1652..2673 ... A022130;
Antidiagonal rows (T(n, k)):
1;
2, 4;
3, 7, 6;
5, 11, 9, 10;
8, 18, 15, 17, 12;
13, 29, 24, 27, 19, 14;
21, 47, 39, 44, 31, 23, 16;
34, 76, 63, 71, 50, 37, 25, 20;
55, 123, 102, 115, 81, 60, 41, 33, 22;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Casey Mongoven, Nov 07 2011
EXTENSIONS
More terms added by G. C. Greubel, Jun 23 2022
STATUS
approved