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 1-9 of 9 results.

A224659 Number of n X n 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

3, 12, 50, 108, 260, 542, 1126, 2230, 4336, 8246, 15458, 28608, 52420, 95240, 171814, 308056, 549384, 975130, 1723482, 3034498, 5324180, 9311762, 16238070
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 2 of A224665.

Examples

			Some solutions for n=3:
..1..0..0....1..0..0....1..1..2....1..0..1....1..0..2....1..0..0....1..1..1
..0..0..0....1..0..1....0..0..0....1..0..1....0..0..1....0..0..0....0..0..0
..2..1..1....2..0..1....0..1..1....0..0..1....0..0..1....0..1..1....1..1..1

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) for n>10.
Empirical g.f.: x*(3 - 6*x + 14*x^2 - 63*x^3 + 116*x^4 - 80*x^5 + 7*x^6 + 12*x^8 + 3*x^9) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 17 2018

A224666 Number of 4 X 4 0..n matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

78, 108, 142, 180, 222, 268, 318, 372, 430, 492, 558, 628, 702, 780, 862, 948, 1038, 1132, 1230, 1332, 1438, 1548, 1662, 1780, 1902, 2028, 2158, 2292, 2430, 2572, 2718, 2868, 3022, 3180, 3342, 3508, 3678, 3852, 4030, 4212, 4398, 4588, 4782, 4980, 5182
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Examples

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

Links

Crossrefs

Row 4 of A224665.

Formula

Empirical: a(n) = 2*n^2 + 24*n + 52.
Conjectures from Colin Barker, Sep 02 2018: (Start)
G.f.: 2*x*(39 - 63*x + 26*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A224667 Number of 5 X 5 0..n matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

196, 260, 332, 412, 500, 596, 700, 812, 932, 1060, 1196, 1340, 1492, 1652, 1820, 1996, 2180, 2372, 2572, 2780, 2996, 3220, 3452, 3692, 3940, 4196, 4460, 4732, 5012, 5300, 5596, 5900, 6212, 6532, 6860, 7196, 7540, 7892, 8252, 8620, 8996, 9380, 9772, 10172
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Examples

			Some solutions for n=3:
..0..1..0..0..1....1..0..1..0..0....1..0..1..0..0....1..0..1..0..0
..0..1..0..0..1....1..0..1..0..1....1..0..1..0..1....1..0..1..0..0
..0..1..0..0..1....0..0..1..0..1....1..0..1..0..1....1..0..1..0..0
..0..1..0..0..1....0..0..1..0..1....1..0..1..0..1....1..0..1..0..1
..0..1..0..0..1....0..0..1..0..1....0..0..1..0..1....2..0..1..0..1

Links

Crossrefs

Row 5 of A224665.

Formula

Empirical: a(n) = 4*n^2 + 52*n + 140.
Conjectures from Colin Barker, Sep 02 2018: (Start)
G.f.: 4*x*(49 - 82*x + 35*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A224668 Number of 6 X 6 0..n matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

428, 542, 668, 806, 956, 1118, 1292, 1478, 1676, 1886, 2108, 2342, 2588, 2846, 3116, 3398, 3692, 3998, 4316, 4646, 4988, 5342, 5708, 6086, 6476, 6878, 7292, 7718, 8156, 8606, 9068, 9542, 10028, 10526, 11036, 11558, 12092, 12638, 13196, 13766, 14348
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Examples

			Some solutions for n=3:
..1..0..0..0..1..0....1..1..1..1..1..0....1..0..1..0..0..3....1..0..1..0..0..1
..1..0..0..0..1..0....0..0..0..0..0..0....1..0..1..0..0..1....1..0..1..0..0..1
..1..0..0..0..1..0....1..1..1..1..1..1....0..0..1..0..0..1....1..0..1..0..0..1
..1..0..0..0..1..0....0..0..0..0..0..0....0..0..1..0..0..1....1..0..1..0..0..1
..1..0..0..0..1..0....1..1..1..1..1..1....0..0..1..0..0..1....1..0..1..0..0..1
..2..0..0..0..1..0....0..0..0..0..0..0....0..0..1..0..0..1....0..0..1..0..0..1

Links

Crossrefs

Row 6 of A224665.

Formula

Empirical: a(n) = 6*n^2 + 96*n + 326.
Conjectures from Colin Barker, Sep 02 2018: (Start)
G.f.: 2*x*(214 - 371*x + 163*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A224660 Number of n X n 0..3 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

4, 16, 72, 142, 332, 668, 1356, 2634, 5046, 9480, 17594, 32286, 58730, 106028, 190204, 339322, 602416, 1064888, 1875104, 3290166, 5754586, 10035236, 17452462, 30275242, 52395822
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 3 of A224665.

Examples

			Some solutions for n=3:
..1..0..1....1..0..0....1..0..0....1..1..0....1..1..3....1..0..2....1..1..1
..0..0..1....1..0..0....0..0..0....0..0..0....0..0..0....1..0..1....0..0..0
..0..0..1....2..0..0....2..1..1....3..1..1....0..1..1....0..0..1....2..1..1

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) for n>10.

A224661 Number of n X n 0..4 matrices with each 2X2 subblock idempotent.

Original entry on oeis.org

5, 20, 98, 180, 412, 806, 1606, 3070, 5808, 10798, 19866, 36184
Offset: 1

Views

Author

R. H. Hardin Apr 14 2013

Keywords

Comments

Column 4 of A224665

Examples

			Some solutions for n=3
..1..0..2....1..0..3....0..0..0....0..0..0....1..0..0....1..1..0....0..0..0
..1..0..1....1..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..4..0..1....2..0..1....2..1..1....0..0..0....0..0..1....0..0..1....4..1..1

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) for n>10

A224662 Number of n X n 0..5 matrices with each 2X2 subblock idempotent.

Original entry on oeis.org

6, 24, 128, 222, 500, 956, 1876, 3538, 6622, 12200, 22274, 40302, 72418, 129332, 229780, 406378, 715800, 1256248, 2197512, 3832510, 6665570, 11563364, 20012598
Offset: 1

Views

Author

R. H. Hardin Apr 14 2013

Keywords

Comments

Column 5 of A224665

Examples

			Some solutions for n=3
..0..0..0....1..1..4....1..0..5....1..1..3....1..0..2....1..0..2....1..0..0
..0..0..0....0..0..0....1..0..1....0..0..0....1..0..1....1..0..1....1..0..1
..2..1..1....0..0..0....0..0..1....5..1..1....2..0..1....4..0..1....3..0..1

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) for n>10

A224663 Number of n X n 0..6 matrices with each 2X2 subblock idempotent.

Original entry on oeis.org

7, 28, 162, 268, 596, 1118, 2166, 4038, 7488, 13686, 24818, 44640, 79796, 141848, 250966, 442168, 776152, 1357850, 2368298, 4119186
Offset: 1

Views

Author

R. H. Hardin Apr 14 2013

Keywords

Comments

Column 6 of A224665

Examples

			Some solutions for n=3
..1..1..2....1..1..6....1..1..4....0..0..0....0..1..0....1..1..0....1..0..3
..0..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..0..0....1..0..1
..2..1..1....3..1..1....6..1..1....4..1..1....0..1..0....0..0..1....2..0..1

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) for n>10

A224664 Number of n X n 0..7 matrices with each 2X2 subblock idempotent.

Original entry on oeis.org

8, 32, 200, 318, 700, 1292, 2476, 4570, 8406, 15256, 27498, 49198, 87530, 154940, 273084, 479466, 838944, 1463400, 2545472, 4416198, 7643450, 13199732, 22747870, 39126778, 67176430
Offset: 1

Views

Author

R. H. Hardin Apr 14 2013

Keywords

Comments

Column 7 of A224665

Examples

			Some solutions for n=3
..1..0..0....1..0..4....1..1..6....1..1..5....1..0..0....1..0..6....1..1..2
..1..0..0....0..0..1....0..0..0....0..0..0....1..0..1....1..0..1....0..0..0
..4..0..0....0..0..1....0..1..1....0..0..1....1..0..1....2..0..1....7..1..1

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) for n>10
Empirical g.f.: 8*x -2*x^2 *(-16 -4*x +249*x^2 -516*x^3 +238*x^4 +241*x^5 -199*x^6 -31*x^7 +35*x^8) /(x-1)^3 /(x^2+x-1)^3 . - R. J. Mathar, Nov 09 2018
Showing 1-9 of 9 results.

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