A298715 Number of nX4 0..1 arrays with every element equal to 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 5, 13, 59, 346, 2246, 13650, 87117, 550582, 3489783, 22151146, 140554255, 891978232, 5661362187, 35930336202, 228040023568, 1447314125762, 9185725194376, 58299474631379, 370012068242202, 2348373088230451

Offset

1,2

Comments

Column 4 of A298719.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +21*a(n-2) +26*a(n-3) -83*a(n-4) -381*a(n-5) -615*a(n-6) +35*a(n-7) +3867*a(n-8) +7013*a(n-9) -10556*a(n-10) -28387*a(n-11) +36768*a(n-12) +76311*a(n-13) -45835*a(n-14) +3816*a(n-15) +97956*a(n-16) -117608*a(n-17) -52644*a(n-18) -747689*a(n-19) -1709818*a(n-20) -645060*a(n-21) -356415*a(n-22) +1628581*a(n-23) +4221676*a(n-24) +2300743*a(n-25) +1249904*a(n-26) +3932427*a(n-27) +17279908*a(n-28) +9184386*a(n-29) -17055518*a(n-30) +1579068*a(n-31) +5489858*a(n-32) -25487233*a(n-33) -17021794*a(n-34) -4854033*a(n-35) -41985127*a(n-36) -27002556*a(n-37) -21698789*a(n-38) -3750642*a(n-39) -47747959*a(n-40) -17666861*a(n-41) +21595450*a(n-42) -9559888*a(n-43) -13055872*a(n-44) -8853708*a(n-45) +8773297*a(n-46) +25433464*a(n-47) -139020*a(n-48) -17186112*a(n-49) +22110645*a(n-50) -10615240*a(n-51) +6879505*a(n-52) -2098646*a(n-53) +217015*a(n-54) -319802*a(n-55) -196014*a(n-56) -101709*a(n-57) +40087*a(n-58) +18226*a(n-59) -14278*a(n-60) +4444*a(n-61) -144*a(n-62) -768*a(n-63) for n>64

Example

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

Crossrefs

Cf. A298719.

Sequence in context: A149565 A149566 A298066 * A380084 A006701 A071699

Adjacent sequences: A298712 A298713 A298714 * A298716 A298717 A298718

Keyword

nonn

Author

R. H. Hardin, Jan 25 2018

Status

approved