A298135 Number of nX4 0..1 arrays with every element equal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 2, 3, 10, 20, 68, 185, 561, 1600, 4856, 14490, 43334, 130046, 390291, 1172586, 3523139, 10593181, 31854446, 95807649, 288198019, 867005085, 2608469794, 7848188504, 23614061363, 71053102045, 213798191069, 643325960937

Offset

1,2

Comments

Column 4 of A298139.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -5*a(n-2) +a(n-3) -19*a(n-4) +15*a(n-5) +77*a(n-7) -84*a(n-8) +104*a(n-9) -175*a(n-10) +237*a(n-11) -444*a(n-12) +166*a(n-13) -252*a(n-14) +783*a(n-15) -239*a(n-16) -923*a(n-17) +47*a(n-18) -1198*a(n-19) +4530*a(n-20) -2018*a(n-21) +8752*a(n-22) -12503*a(n-23) +11509*a(n-24) -11694*a(n-25) +12104*a(n-26) -39091*a(n-27) +11361*a(n-28) +13063*a(n-29) +25473*a(n-30) -18499*a(n-31) -14521*a(n-32) +40263*a(n-33) -2644*a(n-34) -22026*a(n-35) -35689*a(n-36) +31132*a(n-37) +18644*a(n-38) +6559*a(n-39) -15323*a(n-40) -3234*a(n-41) -21417*a(n-42) -5870*a(n-43) +16627*a(n-44) +9301*a(n-45) +860*a(n-46) -5387*a(n-47) +839*a(n-48) +447*a(n-49) +1998*a(n-50) -1505*a(n-51) -218*a(n-52) -195*a(n-53) +391*a(n-54) -74*a(n-55) -24*a(n-56) -48*a(n-57) +28*a(n-58) +8*a(n-59) -4*a(n-60) for n>61

Example

Some solutions for n=7
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..0..1..0..1. .1..0..1..0. .1..0..1..0. .1..0..0..1. .1..0..0..1
..0..0..0..1. .1..0..1..0. .1..1..0..0. .1..1..1..0. .1..1..1..0
..0..1..1..0. .0..1..1..0. .1..0..1..0. .0..0..0..1. .1..0..1..0
..1..0..0..1. .1..0..1..0. .1..0..1..0. .0..1..1..0. .1..0..0..1
..1..1..1..1. .1..1..0..0. .1..1..0..0. .1..1..0..0. .1..1..1..1

Crossrefs

Cf. A298139.

Sequence in context: A148055 A089791 A297872 * A226356 A141050 A354720

Adjacent sequences: A298132 A298133 A298134 * A298136 A298137 A298138

Keyword

nonn

Author

R. H. Hardin, Jan 13 2018

Status

approved