A298837 Number of nX4 0..1 arrays with every element equal to 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 6, 21, 110, 1045, 7322, 60497, 482261, 3886764, 31419679, 253669718, 2050750767, 16574522884, 133980763315, 1083047418757, 8754987461582, 70773060189635, 572110944739376, 4624804772439213, 37385796035240692, 302217747405919419

Offset

1,2

Comments

Column 4 of A298841.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) +17*a(n-2) -195*a(n-3) -301*a(n-4) +2160*a(n-5) +2724*a(n-6) -12908*a(n-7) -15160*a(n-8) +47906*a(n-9) +54649*a(n-10) -121788*a(n-11) -119168*a(n-12) +219680*a(n-13) +109795*a(n-14) -358602*a(n-15) +332162*a(n-16) +436116*a(n-17) -1047261*a(n-18) -907623*a(n-19) +1904805*a(n-20) +943907*a(n-21) -401499*a(n-22) -3080376*a(n-23) +756838*a(n-24) +2344863*a(n-25) -422428*a(n-26) -154363*a(n-27) -1739231*a(n-28) +1061307*a(n-29) +880883*a(n-30) -496873*a(n-31) -39576*a(n-32) -190649*a(n-33) +102350*a(n-34) -69812*a(n-35) -105271*a(n-36) +28788*a(n-37) +64379*a(n-38) +25435*a(n-39) -45832*a(n-40) -6076*a(n-41) +16110*a(n-42) +1038*a(n-43) -3416*a(n-44) +408*a(n-45) for n>48

Example

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

Crossrefs

Cf. A298841.

Sequence in context: A026650 A347948 A364328 * A009253 A374836 A365880

Adjacent sequences: A298834 A298835 A298836 * A298838 A298839 A298840

Keyword

nonn

Author

R. H. Hardin, Jan 27 2018

Status

approved