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.

A224543 Number of (n+1) X (n+1) 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

8, 32, 78, 196, 428, 916, 1858, 3678, 7096, 13458, 25150, 46466, 85028, 154356, 278298, 498792, 889320, 1578248, 2789166, 4910498, 8615348, 15067462, 26274538, 45693286
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Diagonal of A224550.

Examples

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

Crossrefs

Cf. A224550.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9).
Empirical g.f.: 2*x*(4 - 8*x - 9*x^2 + 36*x^3 - 34*x^4 + 11*x^5 - 5*x^6 + 7*x^7 + x^8) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Aug 30 2018

A224544 Number of (n+1) X 3 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

16, 32, 52, 86, 137, 218, 345, 547, 869, 1385, 2214, 3549, 5702, 9178, 14794, 23872, 38551, 62292, 100695, 162821, 263331, 425947, 689052, 1114751, 1803532, 2917988, 4721200, 7638842, 12359669, 19998110, 32357349, 52354999, 84711857, 137066333
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Column 2 of A224550.

Examples

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

Links

Crossrefs

Cf. A224550.

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*(16 - 32*x + 4*x^2 + 22*x^3 - 11*x^4) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

A224545 Number of (n+1) X 4 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

28, 52, 78, 125, 193, 302, 472, 743, 1175, 1868, 2982, 4777, 7673, 12350, 19908, 32127, 51887, 83848, 135550, 219193, 354517, 573462, 927708, 1500875, 2428263, 3928792, 6356682, 10285073, 16641325, 26925938, 43566772, 70492187, 114058403
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Column 3 of A224550.

Examples

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

Links

Crossrefs

Cf. A224550.

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*(28 - 60*x + 10*x^2 + 45*x^3 - 25*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

A224546 Number of (n+1) X 5 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

48, 86, 125, 196, 294, 448, 682, 1049, 1626, 2543, 4007, 6355, 10131, 16216, 26035, 41894, 67524, 108962, 175976, 284371, 459720, 743401, 1202365, 1944941, 3146409, 5090378, 8235737, 13324984, 21559506, 34883188, 56441302, 91323005, 147762726
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Column 4 of A224550.

Examples

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

Links

Crossrefs

Cf. A224550.

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*(48 - 106*x + 21*x^2 + 78*x^3 - 47*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

A224547 Number of (n+1) X 6 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

80, 137, 193, 294, 428, 635, 943, 1420, 2162, 3333, 5193, 8166, 12936, 20611, 32983, 52952, 85210, 137349, 221653, 357998, 578544, 935327, 1512543, 2446424, 3957398, 6402125, 10357693, 16757850, 27113432, 43869023, 70980043, 114846496
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Column 5 of A224550.

Examples

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

Links

Crossrefs

Cf. A224550.

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*(80 - 183*x + 45*x^2 + 127*x^3 - 80*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

A224548 Number of (n+1) X 7 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

132, 218, 302, 448, 635, 916, 1323, 1941, 2887, 4363, 6688, 10383, 16288, 25764, 41012, 65594, 105273, 169374, 272985, 440519, 711477, 1149773, 1858822, 3005953, 4861910, 7864766, 12723338, 20584516, 33304007, 53884408, 87184023, 141063753
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Column 6 of A224550.

Examples

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

Links

Crossrefs

Cf. A224550.

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*(132 - 310*x + 90*x^2 + 198*x^3 - 129*x^4 + 10*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 31 2018

A224549 Number of (n+1) X 8 0..1 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

216, 345, 472, 682, 943, 1323, 1858, 2652, 3845, 5681, 8544, 13062, 20247, 31739, 50190, 79892, 127789, 205117, 330056, 532022, 858611, 1386835, 2241302, 3623632, 5860053, 9478413, 15332788, 24805102, 40131355, 64929471, 105053374, 169974912
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2013

Keywords

Comments

Column 7 of A224550.

Examples

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

Links

Crossrefs

Cf. A224550.

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*(216 - 519*x + 172*x^2 + 303*x^3 - 202*x^4 + 15*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 31 2018
Showing 1-7 of 7 results.

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