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.

A224669 Number of (n+1) X 2 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

12, 25, 41, 70, 115, 189, 308, 501, 813, 1318, 2135, 3457, 5596, 9057, 14657, 23718, 38379, 62101, 100484, 162589, 263077, 425670, 688751, 1114425, 1803180, 2917609, 4720793, 7638406, 12359203, 19997613, 32356820, 52354437, 84711261, 137065702
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 1 of A224676.

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3).
Conjectures from Colin Barker, Feb 17 2018: (Start)
G.f.: x*(12 + x - 9*x^2) / ((1 - x)*(1 - x - x^2)).
a(n) = -4 + (2^(-1-n)*((1-sqrt(5))^n*(-19+13*sqrt(5)) + (1+sqrt(5))^n*(19+13*sqrt(5)))) / sqrt(5).
(End)

A224670 Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

25, 50, 76, 123, 191, 300, 470, 741, 1173, 1866, 2980, 4775, 7671, 12348, 19906, 32125, 51885, 83846, 135548, 219191, 354515, 573460, 927706, 1500873, 2428261, 3928790, 6356680, 10285071, 16641323, 26925936, 43566770, 70492185, 114058401
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 2 of A224676.

Examples

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

Links

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5).
Conjectures from Colin Barker, Feb 17 2018: (Start)
G.f.: x*(25 - 50*x + x^2 + 44*x^3 - 21*x^4) / ((1 - x)^3*(1 - x - x^2)).
a(n) = -2 + 2^(1-n)*sqrt(5)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) + 2*(1+n) + (1+n)*(2+n)/2.
(End)

A224671 Number of (n+1) X 4 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

41, 76, 108, 170, 257, 398, 617, 967, 1525, 2421, 3862, 6185, 9934, 15990, 25778, 41604, 67199, 108600, 175575, 283929, 459235, 742871, 1201788, 1944315, 3145732, 5089648, 8234952, 13324142, 21558605, 34882226, 56440277, 91321915, 147761569
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 3 of A224676.

Examples

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

Links

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.
Conjectures from Colin Barker, Feb 17 2018: (Start)
G.f.: x*(41 - 88*x + 9*x^2 + 77*x^3 - 41*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)).
a(n) = 5 + (2^(-1-n)*((1-sqrt(5))^n*(-19+29*sqrt(5)) + (1+sqrt(5))^n*(19+29*sqrt(5)))) / sqrt(5) + 4*(1+n) + (1+n)*(2+n)/2 for n>1.
(End)

A224672 Number of (n+1) X 5 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

70, 123, 170, 260, 381, 573, 864, 1322, 2043, 3191, 5026, 7972, 12713, 20357, 32696, 52630, 84851, 136951, 221214, 357516, 578017, 934753, 1511920, 2445750, 3956671, 6401343, 10356854, 16756952, 27112473, 43868001, 70978956, 114845342
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 4 of A224676.

Examples

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

Links

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*(70 - 157*x + 28*x^2 + 125*x^3 - 72*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Feb 17 2018

A224673 Number of (n+1) X 6 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

115, 191, 257, 381, 542, 793, 1166, 1746, 2650, 4080, 6355, 9996, 15843, 25257, 40439, 64951, 104556, 168579, 272108, 439556, 710424, 1148626, 1857577, 3004606, 4860457, 7863203, 12721661, 20582721, 33302090, 53882365, 87181850, 141061446
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 5 of A224676.

Examples

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

Links

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.
Conjectures from Colin Barker, Feb 17 2018: (Start)
G.f.: x*(115 - 269*x + 68*x^2 + 193*x^3 - 118*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)).
a(n) = 34 + (2^(-1-n)*((1-sqrt(5))^n*(-11+53*sqrt(5)) + (1+sqrt(5))^n*(11+53*sqrt(5)))) / sqrt(5) + 14*(1+n) + (5/2)*(1 + n)*(2+n) for n>1.
(End)

A224674 Number of (n+1) X 7 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

189, 300, 398, 573, 793, 1126, 1608, 2343, 3471, 5236, 8022, 12457, 19553, 30950, 49300, 78895, 126679, 203888, 328702, 530537, 856989, 1385070, 2239388, 3621563, 5857823, 9476016, 15330218, 24802353, 40128421, 64926346, 105050052, 169971387
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 6 of A224676.

Examples

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

Links

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*(189 - 456*x + 143*x^2 + 292*x^3 - 187*x^4 + 10*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Feb 17 2018

A224675 Number of (n+1) X 8 0..2 matrices with each 2 X 2 subblock idempotent.

Original entry on oeis.org

308, 470, 617, 864, 1166, 1608, 2230, 3157, 4554, 6711, 10083, 15415, 23907, 37504, 59351, 94538, 151300, 242962, 391084, 630551, 1017808, 1644185, 2657457, 4296729, 6948881, 11239898, 18182645, 29415972, 47591594, 77000076, 124583698
Offset: 1

Views

Author

R. H. Hardin, Apr 14 2013

Keywords

Comments

Column 7 of A224676.

Examples

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

Links

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*(308 - 762*x + 277*x^2 + 438*x^3 - 291*x^4 + 15*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Feb 17 2018
Showing 1-7 of 7 results.

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

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