A268809 -id:A268809 - cp's OEIS frontend

A268802 Number of n X n 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

3, 34, 332, 5848, 195384, 12432856, 1508087180, 348686105792, 154172619407288, 130573457756588328, 212323461305457440492, 663970589813116610557692, 3999438097971983178736358520, 46462227980008803491191644654968

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Diagonal of A268809.

			Some solutions for n=4
..2..2..2..2. .0..0..1..2. .2..1..0..0. .0..1..0..0. .1..2..2..1
..1..1..2..2. .1..2..2..2. .2..0..0..0. .1..0..0..0. .2..2..2..2
..2..2..2..2. .2..2..1..2. .1..0..0..1. .0..0..0..1. .1..2..2..1
..1..2..1..2. .2..2..2..2. .0..0..0..0. .0..0..0..0. .2..1..2..1

R. H. Hardin, Table of n, a(n) for n = 1..18

Cf. A268809.

A268803 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

9, 34, 104, 290, 772, 1972, 4914, 12010, 28922, 68836, 162274, 379524, 881712, 2036734, 4681646, 10714994, 24430816, 55516546, 125777028, 284188780, 640549034, 1440572818, 3233256010, 7243375068, 16199546178, 36172883716

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

			Some solutions for n=4:
..0..1. .1..2. .1..0. .1..0. .2..2. .1..1. .0..0. .0..2. .0..0. .2..2
..0..1. .2..1. .2..1. .0..1. .1..2. .0..0. .1..2. .1..2. .0..0. .2..2
..0..0. .2..2. .2..2. .2..2. .2..1. .0..0. .2..2. .2..2. .0..0. .1..2
..1..0. .1..2. .2..2. .2..1. .0..0. .1..0. .1..2. .2..1. .0..0. .0..1

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

Column 2 of A268809.

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6) for n>7.

Empirical g.f.: x*(9 + 16*x + 9*x^2 - 2*x^3 + 2*x^4 + 6*x^5 + 3*x^6) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 15 2019

A268804 Number of nX3 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

24, 104, 332, 1202, 4158, 14308, 48460, 162722, 541744, 1791504, 5889586, 19264864, 62738690, 203528858, 658003018, 2120809106, 6816832928, 21856821554, 69922091542, 223229394256, 711333766468, 2262803472594, 7186710244256

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 3 of A268809.

			Some solutions for n=4
..0..1..2. .0..1..1. .2..2..1. .1..2..2. .1..0..0. .2..0..0. .2..2..2
..0..0..1. .0..0..0. .1..2..2. .2..2..1. .0..1..0. .1..0..0. .2..1..1
..1..0..0. .0..0..0. .2..1..2. .1..2..2. .0..0..1. .0..1..0. .2..2..2
..0..0..0. .1..0..1. .1..2..2. .2..1..1. .0..1..2. .0..0..0. .2..2..1

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

Cf. A268809.

Empirical: a(n) = 2*a(n-1) +9*a(n-2) -2*a(n-3) -33*a(n-4) -42*a(n-5) -14*a(n-6) +10*a(n-7) +8*a(n-8) -a(n-10) for n>12

A268805 Number of nX4 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

60, 290, 1202, 5848, 28452, 135912, 640926, 2990786, 13835892, 63544542, 290056316, 1317009868, 5952527788, 26795651036, 120193389832, 537427198324, 2396207992178, 10656560102448, 47282655935580, 209348341875062

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 4 of A268809.

			Some solutions for n=4
..2..2..2..2. .2..2..2..1. .1..2..1..2. .2..2..1..2. .0..2..2..2
..2..1..2..1. .1..2..1..2. .1..2..2..2. .1..2..1..2. .1..2..1..2
..1..2..2..2. .2..2..2..2. .2..2..2..1. .2..2..2..2. .2..2..2..2
..2..2..1..2. .1..2..2..1. .1..2..2..2. .1..2..1..2. .1..2..2..2

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

Cf. A268809.

Empirical: a(n) = 2*a(n-1) +19*a(n-2) +10*a(n-3) -122*a(n-4) -320*a(n-5) -295*a(n-6) +8*a(n-7) +176*a(n-8) +20*a(n-9) -98*a(n-10) -6*a(n-11) +43*a(n-12) -6*a(n-13) -11*a(n-14) +6*a(n-15) -a(n-16) for n>19

A268806 Number of nX5 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

144, 772, 4158, 28452, 195384, 1316226, 8734264, 57302798, 372342650, 2400532536, 15373692036, 97900054556, 620374078660, 3914367133320, 24605301916568, 154148669247610, 962830699411796, 5997782979007294, 37271323919688010

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 5 of A268809.

			Some solutions for n=4
..0..0..1..0..1. .0..1..0..0..0. .2..1..2..2..1. .1..0..0..1..0
..0..0..0..0..1. .0..0..0..1..0. .2..1..2..2..2. .0..0..1..0..0
..1..0..1..0..0. .0..1..0..0..0. .2..2..2..2..2. .1..0..0..0..1
..0..0..0..0..0. .1..0..0..0..0. .2..1..2..2..2. .0..0..1..0..0

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

Cf. A268809.

Empirical: a(n) = 2*a(n-1) +41*a(n-2) +54*a(n-3) -509*a(n-4) -2182*a(n-5) -2830*a(n-6) +1766*a(n-7) +7914*a(n-8) +2584*a(n-9) -10583*a(n-10) -6092*a(n-11) +11506*a(n-12) +5348*a(n-13) -11688*a(n-14) -620*a(n-15) +9251*a(n-16) -4462*a(n-17) -3137*a(n-18) +4774*a(n-19) -2365*a(n-20) +338*a(n-21) +198*a(n-22) -106*a(n-23) +12*a(n-24) +4*a(n-25) -a(n-26) for n>29

A268807 Number of nX6 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

336, 1972, 14308, 135912, 1316226, 12432856, 115671422, 1062318610, 9657289546, 87052567448, 779167091050, 6932066063186, 61353778718298, 540579543332426, 4744132651089162, 41488807479780664, 361699301828001722

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 6 of A268809.

			Some solutions for n=4
..0..1..0..1..0..0. .1..2..2..2..1..2. .2..1..2..2..2..2. .0..0..1..0..0..1
..1..0..0..0..1..0. .1..2..2..2..2..1. .1..2..2..2..2..2. .0..0..1..0..0..0
..0..0..1..0..0..0. .2..2..2..2..2..2. .2..1..2..2..2..1. .1..0..0..0..0..0
..1..0..0..1..0..1. .2..2..2..2..2..1. .2..2..1..2..2..2. .0..1..0..1..0..0

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

Cf. A268809.

Empirical: a(n) = 2*a(n-1) +83*a(n-2) +210*a(n-3) -1918*a(n-4) -13444*a(n-5) -27431*a(n-6) +22868*a(n-7) +172414*a(n-8) +91292*a(n-9) -572846*a(n-10) -576908*a(n-11) +1569339*a(n-12) +1662464*a(n-13) -4129647*a(n-14) -2739590*a(n-15) +10005684*a(n-16) +128072*a(n-17) -18820309*a(n-18) +14239344*a(n-19) +18275195*a(n-20) -39512592*a(n-21) +16595129*a(n-22) +32600294*a(n-23) -63035320*a(n-24) +55225574*a(n-25) -27556538*a(n-26) +5959238*a(n-27) +1367780*a(n-28) -935764*a(n-29) -205936*a(n-30) +253428*a(n-31) -6946*a(n-32) -44268*a(n-33) +5192*a(n-34) +6896*a(n-35) -1085*a(n-36) -848*a(n-37) +74*a(n-38) +94*a(n-39) +3*a(n-40) -6*a(n-41) -a(n-42) for n>45

A268808 Number of nX7 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

768, 4914, 48460, 640926, 8734264, 115671422, 1508087180, 19390335102, 246666802206, 3110082281974, 38924665296474, 484120668061458, 5988867204857378, 73740656947715536, 904257358969806890

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 7 of A268809.

			Some solutions for n=3
..2..2..2..2..2..1..2. .0..0..0..1..0..0..0. .0..0..1..0..1..0..0
..2..2..2..2..2..2..1. .0..0..0..0..1..0..1. .1..0..0..1..0..0..1
..1..2..1..2..1..0..0. .0..1..0..0..0..0..1. .0..1..0..0..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 68

Cf. A268809.

Empirical recurrence of order 68 (see link above)

cp's OEIS Frontend

A268802 Number of n X n 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A268803 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A268804 Number of nX3 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A268805 Number of nX4 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A268806 Number of nX5 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A268807 Number of nX6 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A268808 Number of nX7 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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Examples

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