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.

A296322 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

Original entry on oeis.org

1, 5, 11, 23, 54, 122, 278, 634, 1438, 3274, 7451, 16943, 38547, 87691, 199477, 453789, 1032300, 2348324, 5342108, 12152500, 27645148, 62888676, 143062485, 325446157, 740342261, 1684169937, 3831239423, 8715507347, 19826499874, 45102377086
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2017

Keywords

Examples

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

Links

Crossrefs

Column 3 of A296327.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) - 2*a(n-4) + 4*a(n-5) - 3*a(n-6) + 2*a(n-7) - a(n-8).
Empirical g.f.: x*(1 + 3*x + 2*x^2 + 2*x^3 + x^4 - x^5 + x^6 - x^7) / ((1 + x^2)*(1 - 2*x - 2*x^3 + 2*x^4 - 2*x^5 + x^6)). - Colin Barker, Feb 23 2019

A296323 Number of nX4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

Original entry on oeis.org

1, 8, 23, 61, 185, 562, 1677, 4998, 14968, 44818, 134061, 401123, 1200360, 3591843, 10747770, 32160619, 96234620, 287963368, 861674203, 2578393448, 7715343389, 23086669802, 69082386936, 206715662599, 618556579000, 1850910743566
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2017

Keywords

Comments

Column 4 of A296327.

Examples

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

Links

Crossrefs

Cf. A296327.

Formula

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +13*a(n-3) -17*a(n-4) +22*a(n-5) -30*a(n-6) +33*a(n-7) -42*a(n-8) +37*a(n-9) -34*a(n-10) +21*a(n-11) -12*a(n-12) +4*a(n-13) -a(n-14)

A296324 Number of n X 5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1's.

Original entry on oeis.org

1, 15, 54, 185, 853, 3569, 14691, 62193, 261763, 1099727, 4630135, 19487541, 82011553, 345200748, 1452975794, 6115623192, 25741334468, 108348131766, 456048653285, 1919560023966, 8079646389293, 34008145665113, 143144156221751
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2017

Keywords

Comments

Column 5 of A296327.

Examples

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

Links

Crossrefs

Cf. A296327.

Formula

Empirical: a(n) = 6*a(n-1) -15*a(n-2) +51*a(n-3) -121*a(n-4) +266*a(n-5) -598*a(n-6) +1026*a(n-7) -1958*a(n-8) +2883*a(n-9) -4421*a(n-10) +5480*a(n-11) -5762*a(n-12) +4485*a(n-13) -1246*a(n-14) -1423*a(n-15) +3587*a(n-16) -2563*a(n-17) +1429*a(n-18) +788*a(n-19) -1333*a(n-20) +2661*a(n-21) -3283*a(n-22) +2331*a(n-23) +1215*a(n-24) -4008*a(n-25) +2878*a(n-26) +724*a(n-27) -2739*a(n-28) +1555*a(n-29) +468*a(n-30) -1080*a(n-31) +418*a(n-32) +204*a(n-33) -249*a(n-34) +54*a(n-35) +44*a(n-36) -29*a(n-37) +a(n-38) +4*a(n-39) -a(n-40).

A296325 Number of nX6 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

Original entry on oeis.org

1, 26, 122, 562, 3569, 20088, 112235, 643541, 3666933, 20890748, 119144071, 679253594, 3873420006, 22088544036, 125956423940, 718274061983, 4096006211974, 23357654042928, 133198547653768, 759573589408188
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2017

Keywords

Comments

Column 6 of A296327.

Examples

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

Links

Crossrefs

Cf. A296327.

Formula

Empirical recurrence of order 83 (see link above)

A296326 Number of nX7 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

Original entry on oeis.org

1, 45, 278, 1677, 14691, 112235, 850404, 6660799, 51754039, 401363520, 3119306759, 24239641260, 188341349284, 1463488096858, 11372085577974, 88367785063892, 686667612240495, 5335806199766372, 41462375276685856, 322187049424431729
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2017

Keywords

Comments

Column 7 of A296327.

Examples

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

Links

Crossrefs

Cf. A296327.

A296321 Number of n X n 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1's.

Original entry on oeis.org

1, 3, 11, 61, 853, 20088, 850404, 72224019, 11207386103, 3245575984755, 1784744625714267, 1830394475306895557, 3517200566091635085954, 12698075318404649075573041, 85871949097296276009847589332
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2017

Keywords

Comments

Diagonal of A296327.

Examples

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

Crossrefs

Cf. A296327.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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