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 1-6 of 6 results.

A299589 Number of n X n 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 5, 23, 113, 576, 2583, 11656, 54738, 252959, 1159927, 5359097, 24760544, 114126327, 526426848, 2429504050, 11207820807, 51702119063, 238537489057, 1100501704736, 5077031912807, 23422773519432, 108060889914594
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2018

Keywords

Comments

Diagonal of A299595.

Examples

			Some solutions for n=5
..0..0..0..0..0. .0..0..1..0..0. .0..0..1..0..0. .0..0..0..0..0
..0..0..0..0..0. .0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0
..1..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0
..0..0..0..0..0. .1..0..0..0..0. .0..0..0..0..0. .0..0..0..0..1
..0..1..0..0..0. .0..0..0..1..0. .0..0..0..1..0. .0..1..0..0..0

Links

Crossrefs

Cf. A299595.

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) +28*a(n-3) -2*a(n-4) -42*a(n-5) -56*a(n-6) +50*a(n-7) -44*a(n-8) +30*a(n-9) -44*a(n-10) +2*a(n-11) +2*a(n-12) -a(n-14) +a(n-15) for n>18.

A299590 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 3, 5, 11, 19, 35, 65, 120, 220, 404, 744, 1369, 2517, 4629, 8515, 15662, 28806, 52982, 97450, 179239, 329671, 606359, 1115269, 2051300, 3772928, 6939496, 12763724, 23476149, 43179369, 79419241, 146074759, 268673370, 494167370, 908915498
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2018

Keywords

Comments

Column 3 of A299595.

Examples

			Some solutions for n=5:
..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..0
..0..0..0. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0
..0..0..0. .0..0..1. .0..0..0. .1..0..0. .0..0..0. .0..0..1. .0..0..0
..0..0..0. .0..0..0. .1..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0
..0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0

Links

Crossrefs

Cf. A299595.

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) for n>8.
Empirical g.f.: x*(3 + 2*x^2 - x^4 + x^7) / ((1 + x^2)*(1 - x - x^2 - x^3)). - Colin Barker, Feb 15 2018

A299591 Number of n X 4 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 5, 11, 23, 53, 121, 250, 533, 1162, 2490, 5327, 11465, 24641, 52882, 113593, 244046, 524134, 1125735, 2418077, 5193785, 11155562, 23961133, 51466258, 110544050, 237437407, 509992017, 1095411137, 2352832034, 5053646321, 10854722326
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2018

Keywords

Comments

Column 4 of A299595.

Examples

			Some solutions for n=5:
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
..1..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .1..0..0..0
..0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0

Links

Crossrefs

Cf. A299595.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.
Empirical g.f.: x*(5 + x^2 - 8*x^3 - x^4 + 12*x^5 + 6*x^6 - 4*x^7 - 3*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Feb 15 2018

A299592 Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 8, 19, 53, 113, 256, 541, 1148, 2488, 5349, 11453, 24617, 52916, 113605, 243988, 524156, 1125805, 2417997, 5193737, 11155712, 23961101, 51466060, 110544232, 237437573, 509991637, 1095411153, 2352832580, 5053645925, 10854721796
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2018

Keywords

Comments

Column 5 of A299595.

Examples

			Some solutions for n=5:
..0..0..1..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..1..0..0
..0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0. .0..0..0..0..1
..0..0..0..0..0. .1..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0
..0..0..1..0..0. .0..1..0..0..0. .0..1..0..0..0. .0..0..0..1..0

Links

Crossrefs

Cf. A299595.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.
Empirical g.f.: x*(8 + 3*x^2 + 2*x^3 + 9*x^4 + 33*x^5 + 10*x^6 - 14*x^7 - 10*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Feb 15 2018

A299593 Number of n X 6 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 15, 35, 121, 256, 576, 1225, 2601, 5625, 12100, 25921, 55696, 119716, 257049, 552049, 1185921, 2547216, 5470921, 11751184, 25240576, 54213769, 116445681, 250114225, 537219684, 1153892961, 2478446656, 5323453444, 11434238761
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2018

Keywords

Comments

Column 6 of A299595.

Examples

			Some solutions for n=5:
..0..0..0..1..0..0. .0..0..0..0..0..0. .0..0..0..1..0..0. .0..0..0..0..0..0
..1..0..0..0..0..1. .1..0..0..0..0..1. .1..0..0..0..0..0. .1..0..0..0..0..1
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0
..0..1..0..0..0..0. .0..0..1..0..0..0. .0..1..0..0..1..0. .0..1..0..0..1..0

Links

Crossrefs

Cf. A299595.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.
Empirical g.f.: x*(13 + 2*x + 7*x^2 + 32*x^3 + 42*x^4 + 92*x^5 + 23*x^6 - 39*x^7 - 29*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Feb 15 2018

A299594 Number of n X 7 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 26, 65, 250, 541, 1225, 2583, 5488, 11899, 25570, 54750, 117697, 252985, 543115, 1166472, 2505919, 5382274, 11560042, 24830445, 53333641, 114554095, 246050920, 528494067, 1135150426, 2438187262, 5236983073, 11248510665, 24160660963
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2018

Keywords

Comments

Column 7 of A299595.

Examples

			Some solutions for n=5:
..0..0..0..1..0..0..0. .0..0..0..0..0..0..0. .0..0..0..0..1..0..0
..0..0..0..0..0..0..0. .0..0..0..0..0..0..0. .0..0..0..0..0..0..0
..0..0..0..0..0..0..0. .0..0..0..0..0..0..0. .1..0..0..0..0..0..1
..1..0..0..0..0..0..0. .0..0..0..0..0..0..0. .0..0..0..0..0..0..0
..0..0..0..0..0..1..0. .0..0..0..0..1..0..0. .0..0..0..0..0..0..0

Links

Crossrefs

Cf. A299595.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.
Empirical g.f.: x*(21 + 5*x + 18*x^2 + 96*x^3 + 127*x^4 + 234*x^5 + 49*x^6 - 102*x^7 - 73*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Feb 15 2018
Showing 1-6 of 6 results.

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