A305638 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

8, 28, 78, 334, 1516, 6329, 27110, 118085, 519355, 2275485, 10007094, 44192714, 194914769, 860631159, 3804114731, 16808740747, 74300020431, 328513615351, 1452355332413, 6421729825720, 28395939285931, 125559090180746

Offset

1,1

Comments

Column 4 of A305642.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) +a(n-2) +36*a(n-3) -249*a(n-4) -61*a(n-5) -301*a(n-6) +4148*a(n-7) +3004*a(n-8) -1897*a(n-9) -32304*a(n-10) -46560*a(n-11) +27683*a(n-12) +137258*a(n-13) +281069*a(n-14) -57027*a(n-15) -342232*a(n-16) -506107*a(n-17) -37426*a(n-18) +554229*a(n-19) -1071467*a(n-20) -898278*a(n-21) +113368*a(n-22) +3803483*a(n-23) +472051*a(n-24) -4424283*a(n-25) +1559246*a(n-26) +3356876*a(n-27) +3532614*a(n-28) -3042945*a(n-29) +6636551*a(n-30) +17850022*a(n-31) +8400099*a(n-32) -11687308*a(n-33) -24486823*a(n-34) -2662032*a(n-35) -24508906*a(n-36) -44534827*a(n-37) -34883725*a(n-38) -8259004*a(n-39) +30416901*a(n-40) +13943043*a(n-41) +32010563*a(n-42) +30849876*a(n-43) +15374803*a(n-44) +40574097*a(n-45) +36979452*a(n-46) +13755094*a(n-47) -15128558*a(n-48) -12893233*a(n-49) -1964205*a(n-50) -2251916*a(n-51) +200153*a(n-52) +283036*a(n-53) +778936*a(n-54) -353165*a(n-55) -1367887*a(n-56) +200589*a(n-57) +542316*a(n-58) +68855*a(n-59) -157236*a(n-60) -100632*a(n-61) +8908*a(n-62) +16806*a(n-63) +1668*a(n-64) -240*a(n-65) for n>67

Example

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

Crossrefs

Cf. A305642.

Sequence in context: A316214 A134638 A293289 * A331757 A130129 A317032

Adjacent sequences: A305635 A305636 A305637 * A305639 A305640 A305641

Keyword

nonn

Author

R. H. Hardin, Jun 07 2018

Status

approved