A298830 Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 16, 6, 68, 141, 489, 2774, 9849, 39101, 183074, 768268, 3094425, 13600466, 58825790, 243388690, 1044751712, 4510287691, 18993143352, 80911731590, 347373816744, 1474949726778, 6275196854211, 26837387067655, 114307141604206

Offset

1,2

Comments

Column 4 of A298834.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +a(n-2) +49*a(n-3) -190*a(n-4) -142*a(n-5) -490*a(n-6) +3529*a(n-7) +931*a(n-8) -2445*a(n-9) -22916*a(n-10) +8373*a(n-11) +46085*a(n-12) +28964*a(n-13) -74055*a(n-14) -166635*a(n-15) +170052*a(n-16) +116703*a(n-17) +83747*a(n-18) -359546*a(n-19) +148326*a(n-20) +463402*a(n-21) -380831*a(n-22) -522218*a(n-23) +118848*a(n-24) +606224*a(n-25) +51024*a(n-26) -315707*a(n-27) -51586*a(n-28) -479161*a(n-29) -4310630*a(n-30) +6488972*a(n-31) -360817*a(n-32) +1226847*a(n-33) +97998*a(n-34) -2001512*a(n-35) -2307*a(n-36) -2820274*a(n-37) +1066042*a(n-38) +1038066*a(n-39) -416347*a(n-40) -1837978*a(n-41) +2558113*a(n-42) -327253*a(n-43) -301655*a(n-44) -874393*a(n-45) +2898299*a(n-46) +1530562*a(n-47) -1350912*a(n-48) -2229129*a(n-49) -648926*a(n-50) +481347*a(n-51) +250281*a(n-52) +86759*a(n-53) +184992*a(n-54) +330267*a(n-55) +26616*a(n-56) -139260*a(n-57) -132100*a(n-58) -965*a(n-59) +23028*a(n-60) +14606*a(n-61) -1538*a(n-62) -504*a(n-63) for n>65

Example

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

Crossrefs

Cf. A298834.

Sequence in context: A161884 A166210 A141078 * A302215 A057964 A302463

Adjacent sequences: A298827 A298828 A298829 * A298831 A298832 A298833

Keyword

nonn

Author

R. H. Hardin, Jan 27 2018

Status

approved