A299570 Number of nX4 0..1 arrays with every element equal to 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

2, 13, 25, 78, 237, 844, 2604, 8136, 26760, 86924, 277835, 899022, 2919889, 9444839, 30500170, 98689584, 319463193, 1033422691, 3342846428, 10816675277, 34999690964, 113237813316, 366379979168, 1185473942356, 3835735125264

Offset

1,1

Comments

Column 4 of A299574.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -25*a(n-2) +50*a(n-3) -91*a(n-4) +124*a(n-5) -120*a(n-6) +111*a(n-7) -117*a(n-8) -57*a(n-9) +1422*a(n-10) -2842*a(n-11) +2995*a(n-12) -4038*a(n-13) +6271*a(n-14) -7029*a(n-15) -1871*a(n-16) -15749*a(n-17) +45068*a(n-18) -29238*a(n-19) -11829*a(n-20) -13467*a(n-21) +121211*a(n-22) +105023*a(n-23) -109380*a(n-24) -364968*a(n-25) +909532*a(n-26) -489713*a(n-27) +105583*a(n-28) -1369411*a(n-29) +1850541*a(n-30) -420304*a(n-31) -5805132*a(n-32) +497842*a(n-33) -3558245*a(n-34) +6905661*a(n-35) +1832173*a(n-36) +5566908*a(n-37) +19899549*a(n-38) -9420347*a(n-39) +14803578*a(n-40) -7946936*a(n-41) -11244317*a(n-42) -1408955*a(n-43) -30465026*a(n-44) -6249506*a(n-45) -34375368*a(n-46) +817988*a(n-47) +14972721*a(n-48) +9589036*a(n-49) +20715181*a(n-50) +4441849*a(n-51) +12903307*a(n-52) -5950420*a(n-53) +252652*a(n-54) -4307590*a(n-55) -1421094*a(n-56) -1915678*a(n-57) -919320*a(n-58) +228232*a(n-59) +276920*a(n-60) +280520*a(n-61) -18928*a(n-62) +26896*a(n-63) -3936*a(n-64) -3264*a(n-65) -1152*a(n-66) +256*a(n-67) for n>68

Example

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

Crossrefs

Cf. A299574.

Sequence in context: A101863 A297955 A298578 * A329630 A018628 A018657

Adjacent sequences: A299567 A299568 A299569 * A299571 A299572 A299573

Keyword

nonn

Author

R. H. Hardin, Feb 13 2018

Status

approved