A303321 Number of nX4 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 8, 1, 2, 4, 3, 3, 10, 9, 10, 19, 29, 40, 65, 96, 148, 238, 356, 573, 865, 1381, 2136, 3369, 5245, 8248, 12925, 20251, 31889, 49995, 78599, 123579, 194464, 305630, 481471, 757704, 1193056, 1879551, 2961524, 4666170, 7355683, 11597513, 18284922

Offset

1,2

Comments

Column 4 of A303325.

Links

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

Formula

Empirical: a(n) = 2*a(n-2) +4*a(n-3) +2*a(n-4) -3*a(n-5) -6*a(n-6) -10*a(n-7) -16*a(n-8) -9*a(n-9) +11*a(n-10) +35*a(n-11) +39*a(n-12) +30*a(n-13) +13*a(n-14) -6*a(n-15) -38*a(n-16) -66*a(n-17) -80*a(n-18) -55*a(n-19) -14*a(n-20) +25*a(n-21) +49*a(n-22) +76*a(n-23) +90*a(n-24) +67*a(n-25) +16*a(n-26) -30*a(n-27) -46*a(n-28) -37*a(n-29) -49*a(n-30) -51*a(n-31) -12*a(n-32) +47*a(n-33) +62*a(n-34) +14*a(n-35) -16*a(n-36) -7*a(n-37) -8*a(n-38) -35*a(n-39) -48*a(n-40) -18*a(n-41) +19*a(n-42) +33*a(n-43) +23*a(n-44) +16*a(n-45) +12*a(n-46) +a(n-47) -6*a(n-48) -11*a(n-49) -8*a(n-50) -3*a(n-51) -a(n-52) +2*a(n-53) +a(n-54) +a(n-55) for n>57

Example

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

Crossrefs

Cf. A303325.

Sequence in context: A222217 A105473 A010518 * A368146 A356022 A077464

Adjacent sequences: A303318 A303319 A303320 * A303322 A303323 A303324

Keyword

nonn

Author

R. H. Hardin, Apr 21 2018

Status

approved