A298578 Number of nX4 0..1 arrays with every element equal to 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

2, 13, 25, 78, 237, 844, 2551, 7941, 25802, 82080, 258039, 822737, 2628312, 8359547, 26575371, 84674430, 269778131, 858987274, 2735603656, 8714789361, 27760710006, 88426843547, 281688270586, 897368531679, 2858705033226, 9106890037086

Offset

1,1

Comments

Column 4 of A298582.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -12*a(n-2) +20*a(n-3) -40*a(n-4) +24*a(n-5) -16*a(n-6) +17*a(n-7) +2*a(n-8) -35*a(n-9) +888*a(n-10) -518*a(n-11) +561*a(n-12) -1985*a(n-13) +352*a(n-14) +1184*a(n-15) -4415*a(n-16) -15823*a(n-17) +10078*a(n-18) -11814*a(n-19) +28636*a(n-20) -71602*a(n-21) +67017*a(n-22) +175544*a(n-23) +129097*a(n-24) -164526*a(n-25) +276657*a(n-26) -168617*a(n-27) +1143099*a(n-28) -1552674*a(n-29) +183029*a(n-30) -466745*a(n-31) -5355615*a(n-32) +87992*a(n-33) -9421360*a(n-34) +9643950*a(n-35) +4769007*a(n-36) +6862457*a(n-37) +22507266*a(n-38) -8384886*a(n-39) +16582290*a(n-40) -19359234*a(n-41) -13421595*a(n-42) -5636826*a(n-43) -31188540*a(n-44) +13998224*a(n-45) -14107677*a(n-46) +3586120*a(n-47) +10261492*a(n-48) +10322871*a(n-49) +13248762*a(n-50) -4087995*a(n-51) +7159113*a(n-52) -7884344*a(n-53) +2366049*a(n-54) -3814248*a(n-55) +114894*a(n-56) -1477857*a(n-57) +200042*a(n-58) +388778*a(n-59) +143476*a(n-60) +165330*a(n-61) -89336*a(n-62) +21844*a(n-63) -12656*a(n-64) -1608*a(n-65) -736*a(n-66) +608*a(n-67) -64*a(n-68) for n>69

Example

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

Crossrefs

Cf. A298582.

Sequence in context: A263537 A101863 A297955 * A299570 A329630 A018628

Adjacent sequences: A298575 A298576 A298577 * A298579 A298580 A298581

Keyword

nonn

Author

R. H. Hardin, Jan 22 2018

Status

approved