A303036 Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

5, 21, 28, 74, 197, 544, 1686, 5252, 16336, 52895, 174633, 585706, 2005396, 6966921, 24490114, 86986183, 311425171, 1121853996, 4061084204, 14755768611, 53766216246, 196333300490, 718099046548, 2629697794146, 9638889966861

Offset

1,1

Comments

Column 4 of A303040.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-1) -4*a(n-2) +17*a(n-3) -73*a(n-4) -27*a(n-5) -86*a(n-6) +412*a(n-7) +715*a(n-8) +717*a(n-9) -678*a(n-10) -2990*a(n-11) -4820*a(n-12) -4520*a(n-13) -1759*a(n-14) +2115*a(n-15) +10728*a(n-16) +26758*a(n-17) +47806*a(n-18) +55437*a(n-19) +28104*a(n-20) -39265*a(n-21) -114473*a(n-22) -130982*a(n-23) -83874*a(n-24) -24037*a(n-25) -59472*a(n-26) -179450*a(n-27) -261480*a(n-28) -146144*a(n-29) +102190*a(n-30) +239624*a(n-31) +64037*a(n-32) -296364*a(n-33) -461631*a(n-34) -174575*a(n-35) +392211*a(n-36) +747124*a(n-37) +685309*a(n-38) +266070*a(n-39) -93667*a(n-40) -163661*a(n-41) -10697*a(n-42) +100455*a(n-43) +76977*a(n-44) -44571*a(n-45) -130982*a(n-46) -137118*a(n-47) -73015*a(n-48) -9401*a(n-49) +21851*a(n-50) +21527*a(n-51) -1519*a(n-52) -8400*a(n-53) -687*a(n-54) -302*a(n-55) +1732*a(n-56) +4267*a(n-57) +3151*a(n-58) +551*a(n-59) -1037*a(n-60) -1149*a(n-61) -351*a(n-62) +325*a(n-63) +201*a(n-64) -52*a(n-65) -62*a(n-66) +4*a(n-67) +13*a(n-68) -a(n-70)

Example

Some solutions for n=5
..0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1
..0..1..0..1. .0..1..0..0. .0..1..0..1. .0..1..0..1. .0..1..1..1
..0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..1..1. .0..1..0..1

Crossrefs

Cf. A303040.

Sequence in context: A303965 A304351 A305914 * A305343 A186304 A316235

Adjacent sequences: A303033 A303034 A303035 * A303037 A303038 A303039

Keyword

nonn

Author

R. H. Hardin, Apr 17 2018

Status

approved