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Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
+10
1
4, 5, 17, 32, 77, 207, 523, 1304, 3307, 8414, 21308, 53961, 136813, 346873, 879204, 2228553, 5649254, 14320348, 36300091, 92016267, 233250975, 591264096, 1498784411, 3799243014, 9630638220, 24412541681, 61882935885, 156866006985
FORMULA
Empirical: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -8*a(n-6) -8*a(n-7) for n>10
EXAMPLE
Some solutions for n=5
..0..0..0. .0..1..1. .0..1..0. .0..1..0. .0..1..1. .0..0..0. .0..1..1
..0..0..0. .1..0..1. .0..0..0. .0..0..0. .1..0..1. .1..0..0. .0..1..1
..0..0..0. .1..1..1. .0..1..0. .1..0..0. .1..1..1. .0..0..0. .0..0..0
..0..1..1. .1..1..1. .0..1..0. .0..0..1. .1..1..0. .0..0..0. .0..0..0
..0..1..1. .1..1..1. .0..0..0. .0..0..0. .1..1..1. .0..1..0. .0..0..0
Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
+10
1
8, 9, 32, 103, 298, 962, 2966, 8756, 26287, 79873, 241656, 729008, 2201471, 6653034, 20101552, 60722489, 183440897, 554200361, 1674289991, 5058110361, 15280857422, 46164569525, 139466343261, 421337009501, 1272887195452, 3845478091572
FORMULA
Empirical: a(n) = 2*a(n-1) +4*a(n-2) -a(n-4) -17*a(n-5) -22*a(n-6) +2*a(n-7) +38*a(n-8) +42*a(n-9) -5*a(n-10) -5*a(n-11) -9*a(n-12) -24*a(n-13) -26*a(n-14) -20*a(n-15) +6*a(n-16) +20*a(n-17) +16*a(n-18) for n>23
EXAMPLE
Some solutions for n=5
..0..0..0..0. .0..1..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..1..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..1..0. .0..1..0..1
..0..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..1..1
..1..0..0..0. .0..0..0..1. .1..1..1..1. .1..0..0..1. .1..1..1..1
..0..0..1..0. .0..1..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1
Number of n X 5 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
+10
1
16, 22, 77, 298, 1188, 4849, 19176, 75681, 302442, 1206813, 4795820, 19085600, 76040894, 302757556, 1205122061, 4798221285, 19105177194, 76064307634, 302837274327, 1205735288772, 4800572406260, 19113025859945, 76096927209491
FORMULA
Empirical: a(n) = 3*a(n-1) +3*a(n-2) +15*a(n-3) -18*a(n-4) -91*a(n-5) -147*a(n-6) +121*a(n-7) +669*a(n-8) +497*a(n-9) -719*a(n-10) -1587*a(n-11) -720*a(n-12) +1486*a(n-13) +2865*a(n-14) +267*a(n-15) -2474*a(n-16) -2477*a(n-17) -1036*a(n-18) +2694*a(n-19) +2715*a(n-20) +347*a(n-21) -2258*a(n-22) -1637*a(n-23) -370*a(n-24) +1054*a(n-25) +1546*a(n-26) +270*a(n-27) -379*a(n-28) -524*a(n-29) -448*a(n-30) -10*a(n-31) +62*a(n-32) +172*a(n-33) +77*a(n-34) +17*a(n-35) +17*a(n-36) -44*a(n-37) -2*a(n-38) +2*a(n-39) -4*a(n-40) for n>47.
EXAMPLE
Some solutions for n=5
..0..1..0..0..0. .0..1..0..0..0. .0..0..1..0..0. .0..0..0..0..0
..0..0..0..0..1. .0..0..0..0..0. .1..0..0..0..0. .0..0..1..1..0
..0..0..0..0..0. .0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0
..0..0..0..1..0. .1..0..0..0..0. .0..1..0..1..0. .0..0..0..0..0
..0..0..0..0..1. .0..0..1..0..0. .1..0..0..0..1. .0..0..1..0..0
Number of nX6 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
+10
1
32, 45, 207, 962, 4849, 25226, 128710, 660871, 3402775, 17536734, 90189989, 464083933, 2390028219, 12302770116, 63317986986, 325946070229, 1677929368349, 8637050520961, 44459022462216, 228858922197372, 1178074204583981
EXAMPLE
Some solutions for n=5
..0..0..0..0..1..0. .0..0..0..0..0..0. .0..0..1..0..0..0. .0..0..0..0..1..0
..0..1..1..0..0..0. .0..0..0..0..1..1. .1..0..0..0..0..0. .0..0..0..0..0..0
..0..0..0..0..0..0. .0..0..0..0..1..1. .0..0..0..1..0..0. .0..0..0..0..0..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..1..0..0..0. .0..0..0..0..1..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .0..1..0..0..0..1
Number of nX7 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
+10
1
64, 101, 523, 2966, 19176, 128710, 842280, 5553315, 36528087, 240890311, 1589377780, 10478113962, 69104073784, 455793498250, 3005985844063, 19825140803190, 130753850843144, 862362210105594, 5687526991833846
EXAMPLE
Some solutions for n=5
..0..1..0..0..1..0..0. .0..0..0..1..0..1..0. .0..0..1..0..0..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..1..0..0..0..0. .0..0..0..0..0..0..0. .0..0..0..1..0..0..0
..0..1..0..0..0..0..1. .1..0..0..1..1..0..0. .0..0..1..0..0..1..0
..0..0..0..0..0..0..0. .0..0..0..0..0..0..0. .0..0..0..0..0..0..1
Number of nXn 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
+10
0
1, 4, 17, 103, 1188, 25226, 842280, 47632142, 4469582265, 707797981908, 187189348152519, 82725002911322885
EXAMPLE
Some solutions for n=5
..0..0..1..0..0. .0..0..1..0..0. .0..0..0..1..0. .0..0..1..0..0
..0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..1
..1..0..0..0..0. .0..0..0..0..1. .0..0..1..0..0. .0..0..0..0..0
..0..0..0..1..0. .0..0..0..0..0. .0..0..0..1..0. .1..0..0..1..0
..0..1..0..0..1. .0..0..0..1..0. .0..0..0..0..1. .0..0..0..0..1
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