A190113 - OEIS

A190113

T(n,k) = number of 2:3:sqrt(13) proportioned triangles on a (n+1) X (k+1) grid.

0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 8, 16, 8, 0, 0, 12, 28, 28, 12, 0, 0, 16, 44, 48, 44, 16, 0, 0, 20, 60, 76, 76, 60, 20, 0, 0, 24, 76, 108, 120, 108, 76, 24, 0, 0, 28, 92, 140, 172, 172, 140, 92, 28, 0, 0, 32, 108, 176, 224, 248, 224, 176, 108, 32, 0, 0, 36, 124, 212, 284, 328, 328, 284

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,8

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..9797

FORMULA

Empirical for columns:

k=2: a(n) = 4*n - 8 for n>1

k=3: a(n) = 16*n - 36 for n>3

k=4: a(n) = 36*n - 112 for n>6

k=5: a(n) = 60*n - 196 for n>6

k=6: a(n) = 108*n - 472 for n>11

k=7: a(n) = 160*n - 768 for n>11

k=8: a(n) = 228*n - 1232 for n>14

k=9: a(n) = 320*n - 1948 for n>16

k=10: a(n) = 432*n - 2956 for n>19

k=11: a(n) = 552*n - 4028 for n>19

k=12: a(n) = 720*n - 5900 for n>24

k=13: a(n) = 896*n - 7848 for n>24

k=14: a(n) = 1100*n - 10348 for n>27

EXAMPLE

Table starts

.0..0...0...0...0...0...0....0....0....0....0....0....0....0....0....0....0

.0..0...4...8..12..16..20...24...28...32...36...40...44...48...52...56...60

.0..4..16..28..44..60..76...92..108..124..140..156..172..188..204..220..236

.0..8..28..48..76.108.140..176..212..248..284..320..356..392..428..464..500

.0.12..44..76.120.172.224..284..344..404..464..524..584..644..704..764..824

.0.16..60.108.172.248.328..420..516..616..720..824..932.1040.1148.1256.1364

.0.20..76.140.224.328.440..568..704..848.1000.1152.1312.1472.1632.1792.1952

.0.24..92.176.284.420.568..736..916.1108.1312.1520.1740.1964.2188.2416.2644

.0.28.108.212.344.516.704..916.1152.1404.1672.1952.2248.2552.2860.3176.3492

.0.32.124.248.404.616.848.1108.1404.1720.2056.2412.2788.3176.3576.3988.4404

Some solutions for n=7 k=5

..3..5....1..2....4..3....1..4....0..3....4..4....4..0....3..3....4..4....3..0

..3..3....1..4....1..0....1..0....2..5....4..1....2..0....0..3....1..4....3..2

..6..5....4..2....2..5....7..4....3..0....6..4....4..3....3..5....4..2....6..0

PROG

(PARI) T(n, k)=2*sum(i=0, n\3, sum(j=0, k\3, ((i!=0) + (j!=0))* (max(0, n+1 - max(3*i, 2*j)) * max(0, k+1 - (3*j+2*i)) + max(0, n+1 - (3*i+2*j)) * max(0, k+1 - max(3*j, 2*i)) ))) \\ Andrew Howroyd, Mar 11 2024

CROSSREFS

Diagonal is A190112.

Cf. A189885.

Sequence in context: A291649 A216060 A230278 * A165727 A284609 A363174

Adjacent sequences: A190110 A190111 A190112 * A190114 A190115 A190116

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 04 2011

STATUS

approved