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.

A282641 Number of nX2 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

4, 11, 27, 76, 201, 537, 1444, 3859, 10339, 27692, 74145, 198577, 531780, 1424091, 3813739, 10213132, 27350713, 73245065, 196149732, 525287779, 1406717235, 3767179500, 10088482321, 27016889761, 72351054724, 193755653291
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Comments

Column 2 of A282647.

Examples

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

Links

Crossrefs

Cf. A282647.

Formula

Empirical: a(n) = a(n-1) +3*a(n-2) +4*a(n-3).
G.f.: -x*(4+7*x+4*x^2)/(-1+x+3*x^2+4*x^3) . - R. J. Mathar, Feb 28 2017

A282642 Number of n X 3 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

7, 27, 99, 413, 1601, 6349, 25153, 99287, 392907, 1553391, 6142251, 24289277, 96042921, 379779797, 1501741049, 5938235583, 23481235283, 92850420759, 367152906387, 1451810964181, 5740809545409, 22700542022605, 89763402870129
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Examples

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

Links

Crossrefs

Column 3 of A282647.

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) + 8*a(n-3) - 5*a(n-4) + 2*a(n-5) - 2*a(n-6).
Empirical g.f.: x*(7 + 13*x + 3*x^2 - 3*x^3 - 2*x^5) / (1 - 2*x - 6*x^2 - 8*x^3 + 5*x^4 - 2*x^5 + 2*x^6). - Colin Barker, Feb 20 2019

A282643 Number of nX4 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

13, 76, 413, 2638, 15460, 92817, 557439, 3332685, 19979228, 119669673, 716821452, 4294298464, 25723862625, 154096718455, 923100717695, 5529722705330, 33125219903271, 198432924637760, 1188690440868116, 7120718914489889
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Comments

Column 4 of A282647.

Examples

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

Links

Crossrefs

Cf. A282647.

Formula

Empirical: a(n) = 2*a(n-1) +16*a(n-2) +45*a(n-3) +16*a(n-4) -2*a(n-5) -51*a(n-6) -35*a(n-7) -23*a(n-8) +7*a(n-9).
Empirical: G.f.: -x*(13+50*x+53*x^2+11*x^3-52*x^4-86*x^5-58*x^6-16*x^7+7*x^8) /(-1+2*x+16*x^2+45*x^3+16*x^4-2*x^5-51*x^6-35*x^7-23*x^8+7*x^9) . - R. J. Mathar, Mar 02 2017

A282644 Number of n X 5 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

24, 201, 1601, 15460, 133118, 1190848, 10614316, 94161619, 838433062, 7454215075, 66292530149, 589611150641, 5243462854609, 46633173607625, 414729611119231, 3688374141775373, 32802445652275246, 291727015058062232, 2594462295371896780, 23073742634349717259
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Comments

Column 5 of A282647.

Examples

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

Links

Crossrefs

Cf. A282647.

Formula

Empirical: a(n) = 4*a(n-1) +31*a(n-2) +127*a(n-3) -103*a(n-4) -166*a(n-5) -1614*a(n-6) +2383*a(n-7) -4797*a(n-8) +13056*a(n-9) -10639*a(n-10) +8408*a(n-11) -11834*a(n-12) +3060*a(n-13) -2498*a(n-14) +4177*a(n-15) +266*a(n-16) +332*a(n-17) -384*a(n-18) +45*a(n-19) +21*a(n-20) +30*a(n-21).

A282645 Number of nX6 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

44, 537, 6349, 92817, 1190848, 15985259, 213392087, 2835418176, 37825158151, 503735487244, 6711044113622, 89413790513675, 1191164876678376, 15869551906444182, 211421699271324253, 2816663462666267647
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Comments

Column 6 of A282647.

Examples

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

Links

Crossrefs

Cf. A282647.

Formula

Empirical: a(n) = 4*a(n-1) +79*a(n-2) +607*a(n-3) +266*a(n-4) -2548*a(n-5) -26560*a(n-6) +34049*a(n-7) -173917*a(n-8) +713268*a(n-9) -558487*a(n-10) +1834672*a(n-11) -3966758*a(n-12) -328020*a(n-13) -5705577*a(n-14) +9446395*a(n-15) +5808617*a(n-16) +12366945*a(n-17) -8694968*a(n-18) -13760206*a(n-19) -12750065*a(n-20) +9273034*a(n-21) +11373048*a(n-22) +1026632*a(n-23) -7957231*a(n-24) -2757451*a(n-25) +2239571*a(n-26) +1981049*a(n-27) -71634*a(n-28) -319923*a(n-29) -48708*a(n-30)

A282646 Number of nX7 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

81, 1444, 25153, 557439, 10614316, 213392087, 4257307148, 84514081303, 1685475197497, 33544066527869, 667927323468328, 13300345031547682, 264815719570028929, 5272968794893979347, 104992034881743428678
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Comments

Column 7 of A282647.

Examples

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

Links

Crossrefs

Cf. A282647.

Formula

Empirical recurrence of order 66 (see link above)

A282640 Number of n X n 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

Original entry on oeis.org

2, 11, 99, 2638, 133118, 15985259, 4257307148, 2506410920603, 3330699748741870, 9838180083513076754, 65038588812750477539631, 960673982564908731679446423, 31695946605234699442469207411170
Offset: 1

Views

Author

R. H. Hardin, Feb 20 2017

Keywords

Comments

Diagonal of A282647.

Examples

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

Crossrefs

Cf. A282647.
Showing 1-7 of 7 results.

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

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