A305219 Number of nX4 0..1 arrays with every element unequal to 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 9, 15, 49, 170, 581, 2184, 7680, 28315, 102908, 375864, 1374468, 5018055, 18347377, 67036712, 245038336, 895604222, 3273509712, 11965243920, 43734676685, 159858697264, 584313110135, 2135780659951, 7806706628138

Offset

1,2

Comments

Column 4 of A305223.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +4*a(n-2) +a(n-3) -12*a(n-4) -29*a(n-5) -55*a(n-6) -57*a(n-7) -86*a(n-8) +132*a(n-9) +461*a(n-10) +978*a(n-11) +2285*a(n-12) +2447*a(n-13) +2681*a(n-14) -5195*a(n-15) -13204*a(n-16) -25311*a(n-17) -29426*a(n-18) -19223*a(n-19) -23315*a(n-20) +35603*a(n-21) +106580*a(n-22) +196351*a(n-23) +134710*a(n-24) +116741*a(n-25) +111111*a(n-26) -87917*a(n-27) -128435*a(n-28) -55749*a(n-29) +147577*a(n-30) -85101*a(n-31) +212134*a(n-32) -342788*a(n-33) -1087796*a(n-34) -2189755*a(n-35) -2015867*a(n-36) -1673398*a(n-37) -4129999*a(n-38) -2797243*a(n-39) -2372528*a(n-40) -1410690*a(n-41) -1178217*a(n-42) -433973*a(n-43) +2223183*a(n-44) +1174280*a(n-45) +1907328*a(n-46) +2450317*a(n-47) +1325887*a(n-48) -315917*a(n-49) -96055*a(n-50) +139247*a(n-51) -415657*a(n-52) -185020*a(n-53) -32750*a(n-54) +235670*a(n-55) -122326*a(n-56) -160760*a(n-57) +145980*a(n-58) -12244*a(n-59) -22120*a(n-60) +6912*a(n-61) +592*a(n-62) +2864*a(n-63) -1152*a(n-64) -192*a(n-65) for n>66

Example

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

Crossrefs

Cf. A305223.

Sequence in context: A020317 A283676 A373652 * A039314 A146584 A276414

Adjacent sequences: A305216 A305217 A305218 * A305220 A305221 A305222

Keyword

nonn

Author

R. H. Hardin, May 27 2018

Status

approved