A268798 -id:A268798 - cp's OEIS frontend

A268791 Number of n X n 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

0, 22, 248, 4800, 168740, 11138352, 1384570516, 325815151556, 145913571668076, 124768928833331732, 204377241703937153076, 642788798787566885184552, 3889478620658657294120765368, 45350632160719542617837369658508

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Diagonal of A268798.

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

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

Cf. A268798.

A268792 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

3, 22, 78, 234, 652, 1714, 4360, 10820, 26366, 63346, 150482, 354196, 827310, 1919884, 4430664, 10175910, 23272918, 53029498, 120435100, 272714858, 615904208, 1387638220, 3119557838, 6999162874, 15675003042, 35046218020

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

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

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

Column 2 of A268798.

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*(3 + 16*x + 25*x^2 + 18*x^3 + 12*x^4 + 8*x^5 + 3*x^6) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 15 2019

A268793 Number of nX3 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

12, 78, 248, 950, 3384, 11948, 41248, 140698, 474472, 1586038, 5262024, 17348096, 56884272, 185647624, 603388088, 1953997896, 6307338900, 20300666174, 65169102416, 208712267048, 666993883320, 2127375490930, 6773070493400

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 3 of A268798.

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

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

Cf. A268798.

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

A268794 Number of nX4 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

36, 234, 950, 4800, 23994, 117062, 561116, 2652936, 12405748, 57490444, 264428454, 1208522850, 5493284922, 24851601802, 111963916212, 502590509990, 2248738675490, 10032298715910, 44640056867750, 198161794087570

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 4 of A268798.

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

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

Cf. A268798.

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

A268795 Number of nX5 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

96, 652, 3384, 23994, 168740, 1158904, 7801688, 51781418, 339641264, 2206871084, 14226779556, 91107781858, 580148670100, 3676143046622, 23194484120032, 145793482383084, 913349363853072, 5704743147188222, 35535874740219072

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 5 of A268798.

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

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

Cf. A268798.

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

A268796 Number of nX6 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

240, 1714, 11948, 117062, 1158904, 11138352, 104971262, 974000420, 8927994302, 81031120788, 729449219322, 6521558348746, 57964319359808, 512593621373638, 4513059897036336, 39580897460175788, 345946165584055346

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 6 of A268798.

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

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

Cf. A268798.

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

A268797 Number of nX7 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

576, 4360, 41248, 561116, 7801688, 104971262, 1384570516, 17967375416, 230262982692, 2921020155826, 36745483472428, 459003330021886, 5699362152372404, 70403795917829390, 865796392149477244

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 7 of A268798.

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

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

Cf. A268798.

Empirical recurrence of order 68 (see link above)

cp's OEIS Frontend

A268791 Number of n X n 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268792 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268793 Number of nX3 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268794 Number of nX4 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268795 Number of nX5 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268796 Number of nX6 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268797 Number of nX7 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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Examples

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