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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.
2
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 27 2018
STATUS
approved