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.

A268633 Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Original entry on oeis.org

3, 24, 120, 504, 1944, 7128, 25272, 87480, 297432, 997272, 3306744, 10865016, 35429400, 114791256, 369882936, 1186176312, 3788111448, 12053081880, 38225488248, 120875192568, 381221761176, 1199453833944, 3765727153080
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 2 of A268639.

Examples

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

Links

Crossrefs

Cf. A268639.

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*(1 + x)^2 / (1 - 3*x)^2.
a(n) = 8*3^(n-2)*(2*n-1) for n>1.
(End)

A268632 Number of n X n 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 24, 840, 47640, 5419992, 1328460312, 725187096504, 897937832100888, 2550310193527246056, 16737195174968513278656, 255111495114527014241534160, 9064348272085612349020943764248, 752834148761621410865592159869765856
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Diagonal of A268639.

Examples

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

Links

Crossrefs

Cf. A268639.

A268634 Number of n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Original entry on oeis.org

12, 120, 840, 5178, 29772, 163878, 875592, 4578186, 23548164, 119570574, 600870336, 2993807250, 14810051580, 72819229974, 356173467576, 1734202809114, 8410141924596, 40641730213278, 195782548631472, 940481337385122
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Examples

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

Links

Crossrefs

Column 3 of A268639.

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*(2 - 2*x^2 + 3*x^3) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 14 2019

A268635 Number of n_X_4 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Original entry on oeis.org

36, 504, 5178, 47640, 412740, 3440052, 27906474, 221913216, 1737860310, 13445785116, 103012659468, 782824552488, 5908380409134, 44334271544616, 330997648937706, 2460394469263680, 18218335277707956, 134439600276305244
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Examples

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

Links

Crossrefs

Column 4 of A268639.

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*(6 - 24*x + 17*x^2 + 38*x^3 - 27*x^4 - 12*x^5 + 8*x^6) / (1 - 9*x + 15*x^2 - 6*x^3)^2. - Colin Barker, Jan 14 2019

A268636 Number of nX5 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Original entry on oeis.org

96, 1944, 29772, 412740, 5419992, 68710116, 849572724, 10310685036, 123340687488, 1458578214948, 17087534233740, 198629587902636, 2293776106412328, 26339884438238244, 300996939426028068
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 5 of A268639.

Examples

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

Links

Crossrefs

Cf. A268639.

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)

A268637 Number of nX6 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Original entry on oeis.org

240, 7128, 163878, 3440052, 68710116, 1328460312, 25093766490, 465757993812, 8527096170390, 154406753980596, 2770879234068744, 49351916066147196, 873425626212657504, 15373652306609086368, 269322517606253198046
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 6 of A268639.

Examples

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

Links

Crossrefs

Cf. A268639.

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

A268638 Number of n X 7 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totaling two exactly once.

Original entry on oeis.org

576, 25272, 875592, 27906474, 849572724, 25093766490, 725187096504, 20612084839848, 578250487434612, 16051896344807322, 441734555450215308, 12067989070909055082, 327659984810446438932, 8849194102430720956704
Offset: 1

Views

Author

R. H. Hardin, Feb 09 2016

Keywords

Comments

Column 7 of A268639.

Examples

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

Links

Crossrefs

Cf. A268639.

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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