A316879 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

8, 28, 105, 452, 2401, 11532, 54613, 268142, 1322178, 6448163, 31571732, 155259809, 761566882, 3736254465, 18352493470, 90106217668, 442390202621, 2172549312060, 10668437072408, 52387940298962, 257266803546723, 1263369837323884

Offset

1,1

Comments

Column 4 of A316883.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) +45*a(n-3) -421*a(n-4) -18*a(n-5) -269*a(n-6) +11948*a(n-7) +1592*a(n-8) -18934*a(n-9) -181677*a(n-10) -25135*a(n-11) +457553*a(n-12) +1582248*a(n-13) +282*a(n-14) -4433748*a(n-15) -7474093*a(n-16) +2884171*a(n-17) +19900509*a(n-18) +13435654*a(n-19) -23152625*a(n-20) -34719968*a(n-21) +33376426*a(n-22) +79688089*a(n-23) -28668829*a(n-24) -211039334*a(n-25) -140926502*a(n-26) +183777784*a(n-27) +370867409*a(n-28) +176078945*a(n-29) -117563377*a(n-30) -216310254*a(n-31) -317412851*a(n-32) -321631411*a(n-33) +34862894*a(n-34) +556462778*a(n-35) +443433945*a(n-36) -138088515*a(n-37) -508849584*a(n-38) -95440694*a(n-39) +107798891*a(n-40) +90300396*a(n-41) +6982647*a(n-42) +74492926*a(n-43) +52423902*a(n-44) +19167376*a(n-45) -11313142*a(n-46) -34673630*a(n-47) -27895543*a(n-48) -12664616*a(n-49) -7478433*a(n-50) +6268620*a(n-51) +1259757*a(n-52) +4464150*a(n-53) -253929*a(n-54) +351186*a(n-55) -23730*a(n-56) -22998*a(n-57) +50238*a(n-58) -4510*a(n-59) +1776*a(n-60) -256*a(n-61) for n>63

Example

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

Crossrefs

Cf. A316883.

Sequence in context: A110687 A153365 A317149 * A220710 A260935 A289608

Adjacent sequences: A316876 A316877 A316878 * A316880 A316881 A316882

Keyword

nonn

Author

R. H. Hardin, Jul 15 2018

Status

approved