A277767 -id:A277767 - cp's OEIS frontend

A277761 Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

0, 1, 2, 14, 56, 284, 1304, 6248, 29408, 139472, 659360, 3121376, 14768000, 69887936, 330703232, 1564924544, 7405262336, 35042157824, 165821110784, 784674242048, 3713117739008, 17570663078912, 83145267845120, 393447636985856

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

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

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

Column 2 of A277767.

Empirical: a(n) = 4*a(n-1) + 6*a(n-2) - 12*a(n-3).
Conjectures from Colin Barker, Feb 05 2019: (Start)
G.f.: x^2*(1 - 2*x) / ((1 + 2*x)*(1 - 6*x + 6*x^2)).
a(n) = (3*(-1)^n*2^(2+n) - (-5+sqrt(3))*(3+sqrt(3))^n + (3-sqrt(3))^n*(5+sqrt(3))) / 132.
(End)

A277762 Number of n X 3 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 4, 17, 330, 3666, 46289, 560809, 6883464, 84161576, 1030163755, 12605295745, 154256946272, 1887655962034, 23099627259711, 282674025688925, 3459132503499606, 42330011144976582, 517999809756567289

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Column 3 of A277767.

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

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

Cf. A277767.

Empirical: a(n) = 11*a(n-1) +15*a(n-2) -6*a(n-3) +164*a(n-4) -947*a(n-5) +1147*a(n-6) +106*a(n-7) -215*a(n-8) -374*a(n-9) -134*a(n-10) +168*a(n-11).

A277763 Number of nX4 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 18, 204, 9741, 270291, 8971150, 280603511, 8946059000, 283436060320, 8998418743638, 285487168951921, 9059457397078866, 287466089870053015, 9121814912567142070, 289449332145382072648, 9184699258737221554558

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Column 4 of A277767.

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

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

Cf. A277767.

Empirical: a(n) = 36*a(n-1) -68*a(n-2) -2713*a(n-3) +19931*a(n-4) -62381*a(n-5) +266374*a(n-6) -1845409*a(n-7) +9104329*a(n-8) -30969250*a(n-9) +54500421*a(n-10) +53064621*a(n-11) -345542021*a(n-12) +212559402*a(n-13) +480699801*a(n-14) +192091281*a(n-15) -2417781956*a(n-16) -1829259971*a(n-17) +4066046894*a(n-18) -3571370030*a(n-19) +3097594269*a(n-20) +5886612097*a(n-21) +1760414929*a(n-22) -275686906*a(n-23) -16985592806*a(n-24) +12147734232*a(n-25) -9614561545*a(n-26) +9010271063*a(n-27) +2069102963*a(n-28) -2314404621*a(n-29) -6065137060*a(n-30) +4076313465*a(n-31) +1271741772*a(n-32) -122381968*a(n-33) -1122738002*a(n-34) +138695692*a(n-35) +82444184*a(n-36) +98140208*a(n-37) -28064564*a(n-38) -7818348*a(n-39) -4302760*a(n-40) +3035424*a(n-41) -160928*a(n-42) -59072*a(n-43) -1152*a(n-44) for n>45

A277764 Number of nX5 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 80, 1989, 275018, 20049229, 1762881313, 145416104585, 12253138042478, 1025207978301185, 85977721285058269, 7204885193038036176, 603918178598058203435, 50616585384840289440801, 4242477668915521353604820

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Column 5 of A277767.

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

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

Cf. A277767.

A277765 Number of nX6 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 356, 21141, 7824415, 1487830718, 343944986355, 74591651561541, 16513537201433122, 3631417278822015869, 800314315609344769958, 176252542616326417994974, 38825002002696841996583880

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Column 6 of A277767.

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

R. H. Hardin, Table of n, a(n) for n = 1..92

Cf. A277767.

A277766 Number of nX7 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 1584, 220549, 221983169, 110036582827, 67079817376928, 38224184451654485, 22257182633194608078, 12869705874813306766481, 7458446559929491293690613, 4319259920844964071189461906, 2501924582698962860252708115060

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Column 7 of A277767.

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

R. H. Hardin, Table of n, a(n) for n = 1..17

Cf. A277767.

A277768 Number of 3Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 2, 17, 204, 1989, 21141, 220549, 2292380, 23911889, 249253583, 2597767946, 27078215723, 282249897665, 2942003150449, 30665850885332, 319644266438138, 3331797339053418, 34728844714392948, 361994612635214032

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Row 3 of A277767.

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

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

Cf. A277767.

Empirical: a(n) = 11*a(n-1) -a(n-2) +10*a(n-3) -648*a(n-4) -323*a(n-5) +2443*a(n-6) +9234*a(n-7) -2121*a(n-8) +1974*a(n-9) -6288*a(n-10) +2781*a(n-11) -4959*a(n-12) +757*a(n-13) -898*a(n-14) +2180*a(n-15) +116*a(n-16) +44*a(n-17) -288*a(n-18)

A277769 Number of 4Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 14, 330, 9741, 275018, 7824415, 221983169, 6298326387, 178728649865, 5071423132367, 143902812077769, 4083281399156407, 115864087742823865, 3287671351656190808, 93288470977649320614, 2647082885606708742103

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Row 4 of A277767.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 98

Cf. A277767.

Empirical recurrence of order 98 (see link above)

A277770 Number of 5Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 56, 3666, 270291, 20049229, 1487830718, 110036582827, 8144355400488, 602835463794197, 44616311792079721, 3302197502743906336, 244405001824291326112, 18089091210686721809130, 1338824653239265489456655

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Row 5 of A277767.

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

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

Cf. A277767.

A277771 Number of 6Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

Original entry on oeis.org

0, 284, 46289, 8971150, 1762881313, 343944986355, 67079817376928, 13082674671680942, 2551870774231153918, 497725696443014836641, 97078962056423037413261, 18934823123149797267341357

Offset: 1

R. H. Hardin, Oct 29 2016

nonn

Row 6 of A277767.

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

R. H. Hardin, Table of n, a(n) for n = 1..63

Cf. A277767.

cp's OEIS Frontend

A277761 Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277762 Number of n X 3 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277763 Number of nX4 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277764 Number of nX5 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277765 Number of nX6 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277766 Number of nX7 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277768 Number of 3Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277769 Number of 4Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277770 Number of 5Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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A277771 Number of 6Xn 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

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