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.

A251122 Number of (n+1) X (2+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

21, 40, 69, 117, 193, 315, 510, 823, 1326, 2136, 3442, 5550, 8955, 14458, 23355, 37743, 61015, 98661, 159564, 258097, 417516, 675450, 1092784, 1768032, 2860593, 4628380, 7488705, 12116793, 19605181, 31721631, 51326442, 83047675, 134373690
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A251128.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5).
Empirical g.f.: x*(21 - 44*x + 14*x^2 + 20*x^3 - 12*x^4) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Nov 25 2018

A251123 Number of (n+1) X (3+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

40, 69, 108, 173, 272, 430, 680, 1080, 1721, 2752, 4413, 7093, 11421, 18415, 29722, 48007, 77582, 125424, 202822, 328042, 530639, 858434, 1388803, 2246943, 3635427, 5882025, 9517080, 15398705, 24915356, 40313602, 65228468, 105541548, 170769461
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A251128.

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6.
Empirical g.f.: x*(40 - 91*x + 32*x^2 + 46*x^3 - 29*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Nov 25 2018

A251124 Number of (n+1) X (4+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

72, 117, 173, 266, 401, 612, 938, 1452, 2266, 3565, 5646, 8991, 14379, 23071, 37107, 59788, 96455, 155750, 251656, 406798, 657784, 1063847, 1720828, 2783801, 4503681, 7286457, 11789033, 19074302, 30862061, 49935000, 80795606, 130729056
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A251128.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
Empirical g.f.: x*(72 - 171*x + 65*x^2 + 87*x^3 - 59*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251125 Number of (n+1) X (5+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

125, 193, 272, 401, 580, 854, 1268, 1912, 2921, 4520, 7069, 11153, 17717, 28291, 45350, 72899, 117418, 189392, 305786, 494050, 798599, 1291298, 2088427, 3378131, 5464835, 8841109, 14303948, 23142917, 37444576, 60585050, 98027024, 158609308
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A251128.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
Empirical g.f.: x*(125 - 307*x + 125*x^2 + 153*x^3 - 107*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251126 Number of (n+1) X (6+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

212, 315, 430, 612, 854, 1214, 1743, 2550, 3795, 5747, 8835, 13757, 21640, 34309, 54716, 87638, 140804, 226720, 365621, 590248, 953577, 1541325, 2492185, 4030567, 6519574, 10546719, 17062618, 27605400, 44663810, 72264722, 116923755
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A251128.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
Empirical g.f.: x*(212 - 533*x + 230*x^2 + 255*x^3 - 183*x^4 + 10*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251127 Number of (n+1) X (7+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

354, 510, 680, 938, 1268, 1743, 2420, 3429, 4957, 7321, 11025, 16890, 26241, 41224, 65310, 104116, 166730, 267857, 431290, 695527, 1122859, 1814075, 2932255, 4741268, 7668063, 12403458, 20065220, 32461934, 52519952, 84974211, 137486000
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A251128.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
Empirical g.f.: x*(354 - 906*x + 410*x^2 + 414*x^3 - 302*x^4 + 15*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251121 Number of (n+1)X(n+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

Original entry on oeis.org

10, 40, 108, 266, 580, 1214, 2420, 4702, 8926, 16680, 30766, 56180, 101734, 182956, 327080, 581742, 1030000, 1816290, 3191136, 5588050, 9755530, 16983260, 29489098
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Comments

Diagonal of A251128

Examples

			Some solutions for n=4
..0..0..0..0..1....0..0..0..1..1....0..0..0..1..1....1..0..1..0..1
..0..0..0..0..1....0..0..0..0..0....1..0..0..0..0....1..0..1..0..1
..0..0..0..0..1....1..1..1..1..1....1..0..0..0..0....1..0..1..0..0
..0..0..0..0..0....0..0..0..0..0....1..0..0..0..0....1..0..1..0..0
..1..0..0..0..0....1..1..0..0..0....1..0..0..0..0....1..0..1..0..0
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.