cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A268622 Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

9, 42, 174, 666, 2430, 8586, 29646, 100602, 336798, 1115370, 3661038, 11927898, 38618046, 124357194, 398580750, 1272269754, 4046391774, 12827922858, 40550011182, 127848761370, 402142467582, 1262215953162, 3954013510734
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 2 of A268628.

Examples

			Some solutions for n=8:
..1..0. .0..1. .2..1. .1..2. .2..2. .0..1. .0..0. .0..0. .1..0. .1..0
..2..2. .1..0. .1..0. .2..1. .2..2. .1..0. .0..1. .0..1. .2..2. .0..0
..2..1. .2..1. .2..1. .1..2. .1..2. .2..1. .0..0. .0..0. .1..2. .1..2
..2..2. .2..2. .1..0. .2..2. .2..2. .2..2. .1..0. .0..0. .0..1. .2..1
..2..1. .1..2. .2..1. .2..2. .2..1. .2..1. .0..1. .0..0. .1..0. .1..2
..2..2. .2..2. .1..2. .2..1. .2..2. .2..0. .0..0. .1..0. .2..1. .2..2
..1..2. .1..2. .1..2. .1..2. .0..1. .1..0. .1..0. .2..2. .2..2. .1..2
..2..2. .0..0. .0..1. .2..1. .1..2. .0..0. .0..1. .1..2. .1..2. .0..1

Links

Crossrefs

Cf. A268628.

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>3.
Conjectures from Colin Barker, Mar 21 2018: (Start)
G.f.: 3*x*(3 - x)*(1 - x) / (1 - 3*x)^2.
a(n) = 2*3^(n-2)*(5+8*n) for n>1.
(End)

A268621 Number of n X n 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totaling two no more than once.

Original entry on oeis.org

3, 42, 1086, 55452, 6000978, 1430057208, 767057092212, 938662461734076, 2643885168776274078, 17245474696462104041796, 261641272761781630830646332, 9262823664147270920479995625968, 767111588793900754143144516979246884
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Diagonal of A268628.

Examples

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

Links

Crossrefs

Cf. A268628.

A268623 Number of n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

24, 174, 1086, 6300, 34890, 187224, 982086, 5063964, 25764066, 129678528, 646978302, 3204131172, 15769455258, 77195600520, 376136512950, 1825265294892, 8825528262738, 42536536932432, 204425809550958, 979908028544244
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Examples

			Some solutions for n=6:
..0..0..1. .0..0..0. .2..2..1. .1..0..1. .1..2..1. .1..0..1. .1..0..1
..0..1..2. .1..0..0. .0..1..2. .0..0..0. .0..1..2. .0..1..2. .0..0..0
..2..2..2. .0..1..0. .1..0..1. .1..0..0. .0..0..1. .1..0..1. .1..1..0
..1..2..2. .1..2..1. .0..1..0. .0..0..1. .1..0..0. .2..1..0. .0..0..0
..2..1..2. .0..1..0. .1..0..1. .2..1..0. .2..2..1. .2..0..1. .1..0..0
..1..2..2. .0..1..0. .0..1..2. .1..0..1. .1..2..2. .2..1..2. .2..1..0

Links

Crossrefs

Column 3 of A268628.

Formula

Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).
Empirical g.f.: 6*x*(4 - 11*x + 7*x^2 + x^3) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 14 2019

A268624 Number of n X 4 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

60, 666, 6300, 55452, 467190, 3819654, 30553014, 240364746, 1866503592, 14342680944, 109265781870, 826421076378, 6212333663082, 46453421706210, 345772280726172, 2563402622459652, 18936504080614278, 139446644995253358
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Examples

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

Links

Crossrefs

Column 4 of A268628.

Formula

Empirical: a(n) = 18*a(n-1) - 111*a(n-2) + 282*a(n-3) - 333*a(n-4) + 180*a(n-5) - 36*a(n-6) for n>7.
Empirical g.f.: 6*x*(10 - 69*x + 162*x^2 - 157*x^3 + 87*x^4 - 36*x^5 + 8*x^6) / (1 - 9*x + 15*x^2 - 6*x^3)^2.- Colin Barker, Jan 14 2019

A268625 Number of n X 5 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totaling two no more than once.

Original entry on oeis.org

144, 2430, 34890, 467190, 6000978, 74914554, 915847266, 11018667294, 130903914954, 1539375100362, 17950677440298, 207850445630478, 2392281464029314, 27392205838123482, 312238767991217778
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 5 of A268628.

Examples

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

Links

Crossrefs

Cf. A268628.

Formula

Empirical: a(n) = 32*a(n-1) -386*a(n-2) +2264*a(n-3) -7265*a(n-4) +13512*a(n-5) -14960*a(n-6) +9872*a(n-7) -3776*a(n-8) +768*a(n-9) -64*a(n-10).

A268626 Number of nX6 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

336, 8586, 187224, 3819654, 74914554, 1430057208, 26758514760, 493042858032, 8974328440044, 161737670836314, 2891047134413940, 51321708535136676, 905714517532142694, 15902932976899644264, 277998507169027800234
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 6 of A268628.

Examples

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

Links

Crossrefs

Cf. A268628.

Formula

Empirical: a(n) = 60*a(n-1) -1482*a(n-2) +20016*a(n-3) -167163*a(n-4) +924894*a(n-5) -3537110*a(n-6) +9593166*a(n-7) -18693789*a(n-8) +26218062*a(n-9) -26188161*a(n-10) +18139608*a(n-11) -8262712*a(n-12) +2220864*a(n-13) -266256*a(n-14) for n>15

A268627 Number of nX7 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

768, 29646, 982086, 30553014, 915847266, 26758514760, 767057092212, 21665715966234, 604770363515718, 16719464029955466, 458539471622171262, 12491032205839395768, 338309651358216576312, 9117289065936178169226
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 7 of A268628.

Examples

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

Links

Crossrefs

Cf. A268628.

Formula

Empirical: a(n) = 110*a(n-1) -5243*a(n-2) +144650*a(n-3) -2610593*a(n-4) +33017408*a(n-5) -305811128*a(n-6) +2137462184*a(n-7) -11513372884*a(n-8) +48502300256*a(n-9) -161412354008*a(n-10) +427044616576*a(n-11) -901108804624*a(n-12) +1517344261024*a(n-13) -2035022988048*a(n-14) +2164824966496*a(n-15) -1815145078160*a(n-16) +1189730382208*a(n-17) -603502277248*a(n-18) +234173991424*a(n-19) -68574152448*a(n-20) +14906358784*a(n-21) -2352277504*a(n-22) +260550656*a(n-23) -19140608*a(n-24) +835584*a(n-25) -16384*a(n-26)
Showing 1-7 of 7 results.

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