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.

A295410 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1's.

Original entry on oeis.org

1, 10, 234, 19026, 5741797, 6093564449, 23025368248778, 309978055996363953, 14848281990251202621848, 2531566579339095935434773023, 1536279445900820560553369496441851
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Comments

Diagonal of A295416.

Examples

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

Crossrefs

Cf. A295416.

A295411 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Original entry on oeis.org

4, 36, 234, 1534, 10291, 68613, 457178, 3048314, 20323497, 135493938, 903332290, 6022478907, 40151569213, 267688593389, 1784667144371, 11898290761269, 79325337411332, 528858244821419, 3525872716944031, 23506825387232109
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Examples

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

Crossrefs

Column 3 of A295416.

Formula

Empirical: a(n) = 6*a(n-1) + 28*a(n-3) + 3*a(n-4) + 49*a(n-5) + 33*a(n-6) - 34*a(n-7) - 22*a(n-8).
Empirical g.f.: x*(4 + 12*x + 18*x^2 + 18*x^3 + 67*x^4 + 11*x^5 - 50*x^6 - 22*x^7) / (1 - 6*x - 28*x^3 - 3*x^4 - 49*x^5 - 33*x^6 + 34*x^7 + 22*x^8). - Colin Barker, Feb 22 2019

A295412 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Original entry on oeis.org

7, 126, 1534, 19026, 240439, 3019079, 37927609, 476686533, 5990217198, 75274793595, 945936754846, 11887043481205, 149377582878265, 1877141810399248, 23588956324272434, 296428780394920491
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Comments

Column 4 of A295416.

Examples

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

Crossrefs

Cf. A295416.

Formula

Empirical: a(n) = 9*a(n-1) +23*a(n-2) +218*a(n-3) +534*a(n-4) +1923*a(n-5) +3128*a(n-6) -1379*a(n-7) -8708*a(n-8) -5083*a(n-9) +7804*a(n-10) +9844*a(n-11) -968*a(n-12) -6624*a(n-13) -3072*a(n-14)

A295413 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Original entry on oeis.org

12, 454, 10291, 240439, 5741797, 136204120, 3232240913, 76727059034, 1821136011730, 43225734223547, 1025994483127581, 24352654756464595, 578026399603342686, 13719842910804997191, 325649624449572326065
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Comments

Column 5 of A295416.

Examples

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

Crossrefs

Cf. A295416.

Formula

Empirical: a(n) = 21*a(n-1) -19*a(n-2) +1762*a(n-3) +2976*a(n-4) +54764*a(n-5) +89653*a(n-6) +316576*a(n-7) +287742*a(n-8) -20679825*a(n-9) -44940268*a(n-10) +216658751*a(n-11) +618852508*a(n-12) -1025274808*a(n-13) -4191874824*a(n-14) +2114857458*a(n-15) +17367807580*a(n-16) +1683218669*a(n-17) -47511765414*a(n-18) -24987441190*a(n-19) +79504587457*a(n-20) +79176210027*a(n-21) -35208322572*a(n-22) -87836099993*a(n-23) -122776386003*a(n-24) -111692628042*a(n-25) +74324840678*a(n-26) +161097789530*a(n-27) +201019494411*a(n-28) +270708373108*a(n-29) +140937188144*a(n-30) +164331302880*a(n-31) +50684014656*a(n-32) +53238098432*a(n-33) +9806288896*a(n-34) +9366409216*a(n-35) +837222400*a(n-36) +734003200*a(n-37)

A295414 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Original entry on oeis.org

21, 1632, 68613, 3019079, 136204120, 6093564449, 272714953724, 12210363190599, 546643613178667, 24472619590752067, 1095614774297460793, 49049522462925007446, 2195896628441171409216, 98308031733968098712078
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Comments

Column 6 of A295416.

Examples

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

Crossrefs

Cf. A295416.

Formula

Empirical recurrence of order 78 (see link above)

A295415 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Original entry on oeis.org

37, 5854, 457178, 37927609, 3232240913, 272714953724, 23025368248778, 1945003010538968, 164274708080518128, 13874595126484055272, 1171853104636801040141, 98975023815069258155234
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Comments

Column 7 of A295416.

Examples

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

Crossrefs

Cf. A295416.
Showing 1-6 of 6 results.