A298899 Number of nX5 0..1 arrays with every element equal to 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 3, 3, 10, 32, 120, 471, 2070, 9055, 39809, 178728, 805614, 3628936, 16427863, 74247523, 336094409, 1520856812, 6885288837, 31164948670, 141091227797, 638704784849, 2891500909471, 13090012145416, 59260093885255

Offset

1,2

Comments

Column 5 of A298902.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +14*a(n-2) -10*a(n-3) -74*a(n-4) -174*a(n-5) +92*a(n-6) +550*a(n-7) +284*a(n-8) +2822*a(n-9) +387*a(n-10) -4568*a(n-11) +667*a(n-12) -34031*a(n-13) +14309*a(n-14) -20283*a(n-15) -15631*a(n-16) +126141*a(n-17) -18534*a(n-18) +138037*a(n-19) -92804*a(n-20) -62863*a(n-21) -145683*a(n-22) +145669*a(n-23) -252735*a(n-24) +856599*a(n-25) +603305*a(n-26) -951928*a(n-27) +40836*a(n-28) -1648325*a(n-29) +67746*a(n-30) -2832702*a(n-31) +2920682*a(n-32) +2347923*a(n-33) +2455740*a(n-34) -529807*a(n-35) -3152693*a(n-36) -1484407*a(n-37) -780449*a(n-38) -47439*a(n-39) -945802*a(n-40) +5691923*a(n-41) +2876338*a(n-42) -4570720*a(n-43) -3088139*a(n-44) +889471*a(n-45) +1193058*a(n-46) +289889*a(n-47) +642191*a(n-48) -399302*a(n-49) -564706*a(n-50) +60480*a(n-51) +33698*a(n-52) +64879*a(n-53) +81675*a(n-54) -1730*a(n-55) -6011*a(n-56) -1096*a(n-57) -7487*a(n-58) -2317*a(n-59) -530*a(n-60) -144*a(n-61)

Example

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

Crossrefs

Cf. A298902.

Sequence in context: A049975 A019168 A107299 * A205388 A121446 A302196

Adjacent sequences: A298896 A298897 A298898 * A298900 A298901 A298902

Keyword

nonn

Author

R. H. Hardin, Jan 28 2018

Status

approved