A297947 Number of nX4 0..1 arrays with every element equal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

2, 52, 219, 948, 4258, 19561, 88441, 402245, 1831311, 8330961, 37894374, 172425675, 784486903, 3569125339, 16238621755, 73881624965, 336140947838, 1529351967657, 6958148321122, 31657725977397, 144034249072846, 655317671930897

Offset

1,1

Comments

Column 4 of A297951.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -21*a(n-2) +54*a(n-3) -200*a(n-4) +342*a(n-5) -446*a(n-6) +1223*a(n-7) -807*a(n-8) -1330*a(n-9) +1563*a(n-10) -10480*a(n-11) +24684*a(n-12) -29302*a(n-13) +57265*a(n-14) -78482*a(n-15) +46625*a(n-16) -62084*a(n-17) -8460*a(n-18) +272147*a(n-19) -420190*a(n-20) +976617*a(n-21) -1705350*a(n-22) +2135163*a(n-23) -3355799*a(n-24) +3688408*a(n-25) -3510994*a(n-26) +4120995*a(n-27) -1724506*a(n-28) +485319*a(n-29) -1048327*a(n-30) -4310085*a(n-31) +3179761*a(n-32) +98309*a(n-33) +6473166*a(n-34) -1966316*a(n-35) -3346076*a(n-36) -5649149*a(n-37) +1912190*a(n-38) +2272624*a(n-39) +7702451*a(n-40) -2469037*a(n-41) -1669127*a(n-42) -3107416*a(n-43) -2412890*a(n-44) +2281904*a(n-45) +646517*a(n-46) +1539380*a(n-47) -70041*a(n-48) -487558*a(n-49) -432384*a(n-50) -170359*a(n-51) -114913*a(n-52) +134192*a(n-53) +56535*a(n-54) +31739*a(n-55) +31645*a(n-56) +1402*a(n-57) -8896*a(n-58) -2156*a(n-59) -64*a(n-60) +130*a(n-61) +816*a(n-62) +254*a(n-63) -94*a(n-64) -72*a(n-65) -16*a(n-66) for n>69

Example

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

Crossrefs

Cf. A297951.

Sequence in context: A129742 A080921 A053455 * A298556 A298766 A299563

Adjacent sequences: A297944 A297945 A297946 * A297948 A297949 A297950

Keyword

nonn

Author

R. H. Hardin, Jan 09 2018

Status

approved