A304015 Number of nX4 0..1 arrays with every element unequal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

2, 45, 103, 370, 1318, 4449, 16187, 57097, 204138, 731990, 2619348, 9409831, 33795414, 121433334, 436597037, 1569707036, 5644843684, 20301268685, 73014988681, 262618746090, 944600144394, 3397648654668, 12221222404734

Offset

1,1

Comments

Column 4 of A304019.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +5*a(n-2) +3*a(n-3) -42*a(n-4) -27*a(n-5) -4*a(n-6) +83*a(n-7) +24*a(n-8) -3*a(n-9) +232*a(n-10) +194*a(n-11) +1438*a(n-12) +1407*a(n-13) +1582*a(n-14) -4399*a(n-15) -7038*a(n-16) -9014*a(n-17) -5958*a(n-18) -14519*a(n-19) -29553*a(n-20) -46371*a(n-21) +11909*a(n-22) +112061*a(n-23) +151011*a(n-24) +141703*a(n-25) +125305*a(n-26) +251351*a(n-27) +240610*a(n-28) -121659*a(n-29) -322956*a(n-30) -463764*a(n-31) -1041851*a(n-32) -1189237*a(n-33) -1057419*a(n-34) -387348*a(n-35) +719457*a(n-36) +1207620*a(n-37) +790717*a(n-38) +1256929*a(n-39) +1683975*a(n-40) +1530546*a(n-41) +332136*a(n-42) -694167*a(n-43) -350492*a(n-44) -216807*a(n-45) -829750*a(n-46) -421441*a(n-47) +381647*a(n-48) -405304*a(n-49) -449818*a(n-50) +255431*a(n-51) +186823*a(n-52) -168805*a(n-53) +68643*a(n-54) +106160*a(n-55) -24046*a(n-56) -12538*a(n-57) +6066*a(n-58) -6206*a(n-59) -12632*a(n-60) +728*a(n-61) -990*a(n-62) +2086*a(n-63) +1590*a(n-64) -372*a(n-65) -144*a(n-66) for n>67

Example

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

Crossrefs

Cf. A304019.

Sequence in context: A241762 A343424 A041241 * A279680 A305363 A304955

Adjacent sequences: A304012 A304013 A304014 * A304016 A304017 A304018

Keyword

nonn

Author

R. H. Hardin, May 04 2018

Status

approved