A304152 Number of n X 4 0..1 arrays with every element unequal to 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

0, 18, 42, 346, 1767, 10182, 60352, 350540, 2034140, 11908298, 69366367, 404422900, 2359475306, 13758737304, 80237613315, 467966274418, 2729123464612, 15916133452018, 92823028361780, 541340687856998, 3157085468272805

Offset

1,2

Comments

Column 4 of A304156.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +14*a(n-2) +23*a(n-3) -182*a(n-4) -489*a(n-5) +74*a(n-6) +2583*a(n-7) +5111*a(n-8) -1301*a(n-9) -15692*a(n-10) -25039*a(n-11) +10700*a(n-12) +55471*a(n-13) +39149*a(n-14) -100521*a(n-15) -95976*a(n-16) -11197*a(n-17) -82082*a(n-18) -337230*a(n-19) +200952*a(n-20) +1685850*a(n-21) +901791*a(n-22) +681480*a(n-23) +1540936*a(n-24) +8029675*a(n-25) -5247288*a(n-26) +4848552*a(n-27) +29842842*a(n-28) -2256018*a(n-29) -5910924*a(n-30) +29012517*a(n-31) -26670027*a(n-32) -48312547*a(n-33) +53457989*a(n-34) -33117898*a(n-35) -32241090*a(n-36) +75088419*a(n-37) -46945411*a(n-38) -41862512*a(n-39) +32206472*a(n-40) -37890914*a(n-41) -2679551*a(n-42) +42861993*a(n-43) -25134639*a(n-44) -24710989*a(n-45) +10196327*a(n-46) +5087803*a(n-47) +11182988*a(n-48) +1895982*a(n-49) -13849223*a(n-50) -116091*a(n-51) +8094101*a(n-52) +45155*a(n-53) -2178036*a(n-54) -167941*a(n-55) +2957*a(n-56) -37965*a(n-57) +45830*a(n-58) +10161*a(n-59) -1008*a(n-60) +2226*a(n-61) +413*a(n-62) -380*a(n-63) -138*a(n-64) +8*a(n-65) +8*a(n-66) for n>67.

Example

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

Crossrefs

Cf. A304156.

Sequence in context: A105550 A144737 A333457 * A252747 A067750 A043362

Adjacent sequences: A304149 A304150 A304151 * A304153 A304154 A304155

Keyword

nonn

Author

R. H. Hardin, May 07 2018

Status

approved