A298217 Number of n X 4 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

8, 29, 40, 120, 503, 1492, 4767, 17127, 56292, 185937, 631054, 2112217, 7064306, 23731748, 79558981, 266764528, 894854496, 3000540755, 10063476031, 33751763853, 113185610212, 379602276002, 1273102896061, 4269537734069

Offset

1,1

Comments

Column 4 of A298221.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -11*a(n-2) +32*a(n-3) -138*a(n-4) +224*a(n-5) -368*a(n-6) +1235*a(n-7) -1868*a(n-8) +2080*a(n-9) -5635*a(n-10) +9285*a(n-11) -8454*a(n-12) +16479*a(n-13) -28898*a(n-14) +25968*a(n-15) -40279*a(n-16) +50969*a(n-17) -43414*a(n-18) +79083*a(n-19) -54736*a(n-20) +12979*a(n-21) -105882*a(n-22) +112035*a(n-23) -13439*a(n-24) +255596*a(n-25) -310403*a(n-26) +478633*a(n-27) -930265*a(n-28) +858817*a(n-29) -1702940*a(n-30) +1971247*a(n-31) -2226803*a(n-32) +2552458*a(n-33) -2408058*a(n-34) +2736267*a(n-35) -1588493*a(n-36) +1220759*a(n-37) -400636*a(n-38) -737088*a(n-39) +1659402*a(n-40) -2666348*a(n-41) +3475947*a(n-42) -3391507*a(n-43) +3776859*a(n-44) -3557617*a(n-45) +2063197*a(n-46) -2026150*a(n-47) +771111*a(n-48) -400300*a(n-49) +72335*a(n-50) +401038*a(n-51) -110320*a(n-52) +335466*a(n-53) -209550*a(n-54) +76246*a(n-55) -117724*a(n-56) +33156*a(n-57) -14592*a(n-58) +12184*a(n-59) -1048*a(n-60) +448*a(n-61) -48*a(n-62) for n>65.

Example

Some solutions for n=7
..0..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..0..0
..1..0..0..0. .1..0..0..1. .0..0..1..0. .0..1..0..1. .1..0..0..1
..1..0..1..1. .1..0..0..1. .0..0..1..1. .1..1..0..0. .0..1..1..0
..0..0..1..0. .1..0..1..0. .1..0..1..1. .1..1..1..1. .0..1..1..1
..1..1..1..0. .0..0..0..1. .1..1..1..0. .0..1..0..0. .1..1..0..0
..0..0..1..1. .1..1..0..0. .0..0..1..0. .0..1..0..1. .1..1..0..1
..1..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..0..0. .1..0..1..0

Crossrefs

Cf. A298221.

Sequence in context: A299183 A155578 A115107 * A299093 A299875 A035339

Adjacent sequences: A298214 A298215 A298216 * A298218 A298219 A298220

Keyword

nonn

Author

R. H. Hardin, Jan 15 2018

Status

approved