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.

A295525 Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

2, 10, 29, 87, 280, 876, 2735, 8583, 26900, 84274, 264107, 827651, 2593568, 8127490, 25469197, 79812833, 250109752, 783769936, 2456102483, 7696696911, 24119166438, 75582316528, 236852570799, 742225734425, 2325915393694, 7288729246884
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Column 2 of A295531.

Examples

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

Links

Crossrefs

Cf. A295531.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + 5*a(n-3) - a(n-5) - a(n-6).
Empirical g.f.: x*(2 + 6*x + 5*x^2 - x^3 - 2*x^4 - x^5) / (1 - 2*x - 2*x^2 - 5*x^3 + x^5 + x^6). - Colin Barker, Feb 21 2018

A295526 Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

4, 29, 147, 774, 4080, 21489, 113466, 598374, 3155426, 16642084, 87770692, 462903372, 2441353234, 12875695490, 67906455891, 358138834199, 1888825058236, 9961667898631, 52537860596653, 277084804179135, 1461345928848848
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Column 3 of A295531.

Examples

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

Links

Crossrefs

Cf. A295531.

Formula

Empirical: a(n) = 4*a(n-1) +3*a(n-2) +15*a(n-3) +17*a(n-4) +40*a(n-5) -6*a(n-6) -12*a(n-7) +45*a(n-8) -21*a(n-9) -66*a(n-10) +7*a(n-11) +6*a(n-12) -6*a(n-13) +6*a(n-14) +a(n-15) -3*a(n-16) +a(n-18)

A295527 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

7, 87, 774, 7071, 64189, 588529, 5400933, 49414072, 452274232, 4141178883, 37915462501, 347125927592, 3178043159907, 29096212160166, 266386963989786, 2438870587989546, 22328758454009391, 204428063085791198
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Column 4 of A295531.

Examples

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

Links

Crossrefs

Cf. A295531.

Formula

Empirical: a(n) = 6*a(n-1) +13*a(n-2) +115*a(n-3) +249*a(n-4) +426*a(n-5) -1288*a(n-6) -1624*a(n-7) +5590*a(n-8) +6289*a(n-9) -7886*a(n-10) -8123*a(n-11) +5854*a(n-12) +3323*a(n-13) -13470*a(n-14) -5787*a(n-15) +8339*a(n-16) -8574*a(n-17) -31382*a(n-18) -19075*a(n-19) +1988*a(n-20) +11913*a(n-21) -2666*a(n-22) +8280*a(n-23) +11515*a(n-24) +16869*a(n-25) +5768*a(n-26) -4269*a(n-27) -10768*a(n-28) -4992*a(n-29) +1675*a(n-30) +2329*a(n-31) +1426*a(n-32) -22*a(n-33) +215*a(n-34) +a(n-35) -79*a(n-36) -387*a(n-37) -93*a(n-38) +30*a(n-39) +31*a(n-40) +8*a(n-41) -8*a(n-42) -3*a(n-43) +a(n-45)

A295528 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

12, 280, 4080, 64189, 1012315, 16031147, 253594307, 4003959566, 63279327977, 1000139739583, 15804787030137, 249762291976009, 3947048440634688, 62375786616766976, 985731805754249812, 15577646241372914358
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Column 5 of A295531.

Examples

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

Links

Crossrefs

Cf. A295531.

A295529 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

21, 876, 21489, 588529, 16031147, 437241277, 11938414614, 325438086413, 8875686431050, 242075272701612, 6602021695088725, 180056949233250710, 4910676438495880068, 133928360921171032911, 3652617573522712382545
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Column 6 of A295531.

Examples

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

Links

Crossrefs

Cf. A295531.

A295530 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

37, 2735, 113466, 5400933, 253594307, 11938414614, 563330031268, 26515589323171, 1248681784524804, 58814998591494213, 2770085782332161201, 130464623191695045459, 6144598685123051237293, 289398247960170761817752
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Column 7 of A295531.

Examples

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

Links

Crossrefs

Cf. A295531.

A295524 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1's.

Original entry on oeis.org

1, 10, 147, 7071, 1012315, 437241277, 563330031268, 2154370064869978, 24591601562099287015, 837044464889796587986014, 84914857903369744218835564258
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Diagonal of A295531.

Examples

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

Crossrefs

Cf. A295531.
Showing 1-7 of 7 results.

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

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