A317032 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

8, 28, 82, 354, 1718, 7523, 33798, 153703, 700615, 3182971, 14501028, 66218594, 302024137, 1378726299, 6297606271, 28758102887, 131363006085, 600132606903, 2741576694529, 12525540090248, 57227838857461, 261466316314962

Offset

1,1

Comments

Column 4 of A317036.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) +4*a(n-2) +29*a(n-3) -275*a(n-4) -194*a(n-5) +70*a(n-6) +5359*a(n-7) +5000*a(n-8) -8044*a(n-9) -53898*a(n-10) -62665*a(n-11) +74363*a(n-12) +300836*a(n-13) +383300*a(n-14) -219460*a(n-15) -755823*a(n-16) -828976*a(n-17) +57634*a(n-18) -128498*a(n-19) -2438834*a(n-20) -693356*a(n-21) +4783474*a(n-22) +12417619*a(n-23) +4423012*a(n-24) -7638961*a(n-25) -343603*a(n-26) -4906149*a(n-27) -13991493*a(n-28) -18484152*a(n-29) +354290*a(n-30) +17937031*a(n-31) -3478443*a(n-32) -7344862*a(n-33) +7904399*a(n-34) +23136041*a(n-35) -13069666*a(n-36) -42757687*a(n-37) +3052643*a(n-38) +23773840*a(n-39) +23349301*a(n-40) +1173368*a(n-41) -6977865*a(n-42) -24048458*a(n-43) -36030973*a(n-44) +75111982*a(n-45) +126040017*a(n-46) +55386631*a(n-47) -9613949*a(n-48) -23224552*a(n-49) -18171439*a(n-50) -24171438*a(n-51) -9934266*a(n-52) +5945861*a(n-53) +6823576*a(n-54) +1499075*a(n-55) -2157679*a(n-56) +77860*a(n-57) +893292*a(n-58) -8649*a(n-59) -206808*a(n-60) -167806*a(n-61) -608*a(n-62) +29358*a(n-63) +4308*a(n-64) -240*a(n-65) for n>67

Example

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

Crossrefs

Cf. A317036.

Sequence in context: A305638 A331757 A130129 * A229713 A212516 A005343

Adjacent sequences: A317029 A317030 A317031 * A317033 A317034 A317035

Keyword

nonn

Author

R. H. Hardin, Jul 19 2018

Status

approved