A301665 Number of nX4 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.

2, 23, 118, 564, 2793, 14394, 71564, 359659, 1808256, 9076074, 45607585, 229124216, 1151098126, 5783024867, 29053401570, 145961054556, 733293062029, 3683989357618, 18507978344520, 92982190589347, 467132961135876

Offset

1,1

Comments

Column 4 of A301669.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +15*a(n-2) -6*a(n-3) -91*a(n-4) -75*a(n-5) +327*a(n-6) +398*a(n-7) -880*a(n-8) -1862*a(n-9) -823*a(n-10) +79*a(n-11) +5465*a(n-12) +26064*a(n-13) +45144*a(n-14) -31786*a(n-15) -99377*a(n-16) -89293*a(n-17) +55985*a(n-18) -111034*a(n-19) -138395*a(n-20) +141455*a(n-21) +486139*a(n-22) +96486*a(n-23) -536176*a(n-24) +16636*a(n-25) +98232*a(n-26) +573306*a(n-27) -822404*a(n-28) +47656*a(n-29) +698032*a(n-30) +48550*a(n-31) -264890*a(n-32) -1009366*a(n-33) +282680*a(n-34) +950924*a(n-35) -62788*a(n-36) -370362*a(n-37) +6650*a(n-38) -1020118*a(n-39) +1292800*a(n-40) -896852*a(n-41) +1410204*a(n-42) -572266*a(n-43) -344184*a(n-44) -135916*a(n-45) -198212*a(n-46) +723258*a(n-47) -188503*a(n-48) -34287*a(n-49) -130327*a(n-50) +23396*a(n-51) +62935*a(n-52) -53445*a(n-53) +2017*a(n-54) +6884*a(n-55) +16010*a(n-56) +6076*a(n-57) -4473*a(n-58) -7867*a(n-59) -461*a(n-60) +2650*a(n-61) +830*a(n-62) -536*a(n-63) -391*a(n-64) +73*a(n-65) +91*a(n-66) +12*a(n-67) -13*a(n-68) -3*a(n-69) +a(n-70)

Example

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

Crossrefs

Cf. A301669.

Sequence in context: A143912 A041579 A185830 * A193981 A235594 A053299

Adjacent sequences: A301662 A301663 A301664 * A301666 A301667 A301668

Keyword

nonn

Author

R. H. Hardin, Mar 25 2018

Status

approved