A298450 Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 16, 11, 161, 478, 2459, 15248, 78163, 390424, 2230213, 11957077, 62686390, 343644381, 1857612208, 9915556165, 53695082023, 290087274436, 1558866184902, 8413068514505, 45404547945468, 244554296256136, 1318757750900979

Offset

1,2

Comments

Column 4 of A298454.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +9*a(n-2) +89*a(n-3) -204*a(n-4) -742*a(n-5) -2336*a(n-6) +5414*a(n-7) +16164*a(n-8) +22227*a(n-9) -51019*a(n-10) -155268*a(n-11) -9076*a(n-12) +216908*a(n-13) +348123*a(n-14) -565918*a(n-15) -423553*a(n-16) +2275697*a(n-17) +3018514*a(n-18) -4744310*a(n-19) -10714755*a(n-20) +1120597*a(n-21) +12707044*a(n-22) +14767028*a(n-23) -6781707*a(n-24) -13692035*a(n-25) -12330114*a(n-26) -4671661*a(n-27) +21721296*a(n-28) +14985223*a(n-29) +2432193*a(n-30) -25320474*a(n-31) -22704558*a(n-32) +17445078*a(n-33) +34393194*a(n-34) +3452869*a(n-35) -42645667*a(n-36) +551512*a(n-37) +18308956*a(n-38) -481318*a(n-39) -3378385*a(n-40) +2303479*a(n-41) +23871*a(n-42) -1901808*a(n-43) -170904*a(n-44) +588909*a(n-45) +106391*a(n-46) -40247*a(n-47) -13426*a(n-48) -10996*a(n-49) -462*a(n-50) +308*a(n-51) -40*a(n-52) +40*a(n-53) for n>56

Example

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

Crossrefs

Cf. A298454.

Sequence in context: A217157 A070578 A225842 * A028695 A008665 A076823

Adjacent sequences: A298447 A298448 A298449 * A298451 A298452 A298453

Keyword

nonn

Author

R. H. Hardin, Jan 19 2018

Status

approved