A299889 Number of nX4 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 42, 156, 1308, 9682, 77981, 667784, 5725192, 49894988, 436024084, 3819671165, 33500023708, 293944562757, 2579947488299, 22646800053660, 198806639447126, 1745291213052799, 15321855265489822, 134511069014015019

Offset

1,2

Comments

Column 4 of A299893.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) +16*a(n-2) -203*a(n-3) -620*a(n-4) +2225*a(n-5) +8308*a(n-6) -5727*a(n-7) -61372*a(n-8) -555*a(n-9) +229115*a(n-10) -20680*a(n-11) -1005907*a(n-12) -221976*a(n-13) +3660998*a(n-14) +3541455*a(n-15) -3006749*a(n-16) -3086643*a(n-17) +2386804*a(n-18) -13534778*a(n-19) -37704135*a(n-20) -19019838*a(n-21) +9972387*a(n-22) -9529419*a(n-23) -46779256*a(n-24) -38394683*a(n-25) +10977924*a(n-26) +20681132*a(n-27) -41068141*a(n-28) +26998202*a(n-29) +70848525*a(n-30) +33138285*a(n-31) +65899249*a(n-32) -44861274*a(n-33) -41758960*a(n-34) +68124773*a(n-35) +52543923*a(n-36) +7195475*a(n-37) -11801870*a(n-38) -13863048*a(n-39) +11531342*a(n-40) +17574135*a(n-41) -800006*a(n-42) -1498359*a(n-43) +288546*a(n-44) -1477150*a(n-45) -190816*a(n-46) +193456*a(n-47) -24872*a(n-48) +624*a(n-49) for n>51

Example

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

Crossrefs

Cf. A299893.

Sequence in context: A326384 A263285 A263300 * A092228 A159226 A160329

Adjacent sequences: A299886 A299887 A299888 * A299890 A299891 A299892

Keyword

nonn

Author

R. H. Hardin, Feb 21 2018

Status

approved