A301527 Number of nX4 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 16, 92, 742, 5472, 43211, 339956, 2691202, 21316797, 169011518, 1340378030, 10631856635, 84337029071, 669022950500, 5307252023905, 42101846876713, 333990284907385, 2649519288740820, 21018445659880026, 166737860277894562

Offset

1,2

Comments

Column 4 of A301531.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) +23*a(n-2) -99*a(n-3) -225*a(n-4) +151*a(n-5) +362*a(n-6) +1456*a(n-7) +3621*a(n-8) +2422*a(n-9) -10*a(n-10) -14665*a(n-11) -20439*a(n-12) +4359*a(n-13) -29781*a(n-14) -80899*a(n-15) -121000*a(n-16) -144634*a(n-17) +38378*a(n-18) +203302*a(n-19) +219725*a(n-20) +424985*a(n-21) +348008*a(n-22) +35753*a(n-23) +336863*a(n-24) +816903*a(n-25) +1174827*a(n-26) +1074594*a(n-27) -398928*a(n-28) -2156968*a(n-29) -3717082*a(n-30) -4162840*a(n-31) -2546101*a(n-32) +34124*a(n-33) +2475480*a(n-34) +3451617*a(n-35) +2771935*a(n-36) +1382868*a(n-37) -39455*a(n-38) -1006185*a(n-39) -1122912*a(n-40) -745226*a(n-41) -284326*a(n-42) +21490*a(n-43) +102551*a(n-44) +130999*a(n-45) +99371*a(n-46) +46254*a(n-47) +9756*a(n-48) -5180*a(n-49) -6162*a(n-50) -4655*a(n-51) -3717*a(n-52) -1278*a(n-53) -69*a(n-54) +53*a(n-55) +63*a(n-56) +49*a(n-57) +24*a(n-58) +5*a(n-59) -a(n-60) for n>62

Example

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

Crossrefs

Cf. A301531.

Sequence in context: A153029 A170920 A027938 * A185458 A108676 A304344

Adjacent sequences: A301524 A301525 A301526 * A301528 A301529 A301530

Keyword

nonn

Author

R. H. Hardin, Mar 23 2018

Status

approved