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 1-6 of 6 results.

A202329 Number of (n+1)X(n+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

Original entry on oeis.org

16, 48, 162, 576, 2102, 7790, 29174, 110112, 418134, 1595622, 6113746, 23505358, 90633802, 350351642, 1357278302, 5268292832, 20483876822, 79765662902, 311038321442, 1214362277702, 4746455801882, 18570960418922, 72728638093802
Offset: 1

Views

Author

R. H. Hardin Dec 17 2011

Keywords

Comments

Diagonal of A202335

Examples

			Some solutions for n=5
..0..0..0..0..0..1....0..0..0..0..1..0....0..0..0..0..1..0....0..0..0..0..0..1
..0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..1..0....0..0..0..0..0..1
..0..0..0..0..0..1....0..0..0..0..1..1....0..0..1..1..1..1....0..0..0..0..0..1
..0..0..0..0..0..1....0..0..1..1..1..1....0..0..1..1..1..1....0..0..0..0..1..1
..0..0..0..1..1..1....0..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
..0..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1....1..1..1..1..1..1

Links

Formula

Empirical: (n+1)*(27*n-40)*a(n) = (135*n^2-123*n-100)*a(n-1) - 2*(54*n^2-63*n-10)*a(n-2) - 8*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 19 2012
Another recurrence (empirical): (n+1)*(9*n^2-19*n+8)*a(n) = (45*n^3-68*n^2-13*n+20)*a(n-1) - 2*(2*n-3)*(9*n^2-n-2)*a(n-2). - Vaclav Kotesovec, Oct 26 2012

A202330 Number of (n+1) X 4 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

Original entry on oeis.org

36, 82, 162, 289, 478, 746, 1112, 1597, 2224, 3018, 4006, 5217, 6682, 8434, 10508, 12941, 15772, 19042, 22794, 27073, 31926, 37402, 43552, 50429, 58088, 66586, 75982, 86337, 97714, 110178, 123796, 138637, 154772, 172274, 191218, 211681, 233742
Offset: 1

Views

Author

R. H. Hardin, Dec 17 2011

Keywords

Comments

Column 3 of A202335.

Examples

			Some solutions for n=5:
..0..0..0..1....0..0..0..0....0..0..0..1....0..0..1..0....0..0..1..0
..0..0..0..1....0..0..1..0....0..0..0..1....0..0..1..0....0..0..1..1
..0..0..0..1....0..0..1..0....0..0..0..1....0..0..1..0....0..0..1..1
..0..0..0..1....0..0..1..0....0..1..1..1....0..0..1..0....0..1..1..1
..0..0..1..1....0..0..1..0....1..1..1..1....0..0..1..1....0..1..1..1
..0..1..1..1....0..1..1..1....0..1..1..1....0..0..1..0....1..1..1..1

Links

Crossrefs

Cf. A202335.

Formula

Empirical: a(n) = (1/12)*n^4 + (4/3)*n^3 + (83/12)*n^2 + (44/3)*n + 13.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: x*(36 - 98*x + 112*x^2 - 61*x^3 + 13*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
(End)

A202331 Number of (n+1) X 5 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

Original entry on oeis.org

49, 129, 289, 576, 1052, 1796, 2906, 4501, 6723, 9739, 13743, 18958, 25638, 34070, 44576, 57515, 73285, 92325, 115117, 142188, 174112, 211512, 255062, 305489, 363575, 430159, 506139, 592474, 690186, 800362, 924156, 1062791, 1217561
Offset: 1

Views

Author

R. H. Hardin, Dec 17 2011

Keywords

Comments

Column 4 of A202335.

Examples

			Some solutions for n=5:
..0..0..0..0..0....0..0..0..0..0....0..0..0..1..0....0..0..0..0..0
..0..0..0..1..0....0..0..0..0..0....0..0..0..1..0....0..0..0..0..0
..0..0..0..1..0....0..0..0..0..0....0..0..0..1..1....0..0..0..1..0
..0..0..0..1..0....0..0..0..1..1....0..0..0..1..1....0..0..1..1..1
..0..1..1..1..1....0..0..0..1..1....1..1..1..1..1....1..1..1..1..1
..0..0..0..1..1....0..0..1..1..1....0..0..1..1..1....1..1..1..1..1

Links

Crossrefs

Cf. A202335.

Formula

Empirical: a(n) = (1/60)*n^5 + (3/8)*n^4 + 3*n^3 + (89/8)*n^2 + (1169/60)*n + 15.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: x*(49 - 165*x + 250*x^2 - 203*x^3 + 86*x^4 - 15*x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A202332 Number of (n+1) X 6 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

Original entry on oeis.org

64, 191, 478, 1052, 2102, 3896, 6800, 11299, 18020, 27757, 41498, 60454, 86090, 120158, 164732, 222245, 295528, 387851, 502966, 645152, 819262, 1030772, 1285832, 1591319, 1954892, 2385049, 2891186, 3483658, 4173842, 4974202, 5898356, 6961145
Offset: 1

Views

Author

R. H. Hardin, Dec 17 2011

Keywords

Comments

Column 5 of A202335.

Examples

			Some solutions for n=5:
..0..0..0..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0
..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0
..1..1..1..1..1..1....0..0..0..0..0..1....0..0..0..1..1..1....0..0..0..0..1..1
..1..1..1..1..1..1....0..0..0..0..0..1....1..1..1..1..1..1....0..0..0..0..1..1
..1..1..1..1..1..1....0..0..0..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1

Links

Crossrefs

Cf. A202335.

Formula

Empirical: a(n) = (1/360)*n^6 + (1/12)*n^5 + (17/18)*n^4 + (16/3)*n^3 + (5779/360)*n^2 + (295/12)*n + 17.
Conjectures from Colin Barker, May 28 2018: (Start)
G.f.: x*(64 - 257*x + 485*x^2 - 523*x^3 + 331*x^4 - 115*x^5 + 17*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A202333 Number of (n+1) X 7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

Original entry on oeis.org

81, 270, 746, 1796, 3896, 7790, 14588, 25885, 43903, 71658, 113154, 173606, 259694, 379850, 544580, 766823, 1062349, 1450198, 1953162, 2598312, 3417572, 4448342, 5734172, 7325489, 9280379, 11665426, 14556610, 18040266, 22214106, 27188306
Offset: 1

Views

Author

R. H. Hardin, Dec 17 2011

Keywords

Comments

Column 6 of A202335.

Examples

			Some solutions for n=5:
..0..0..0..0..0..1..1....0..0..0..0..0..1..0....0..0..0..0..0..0..0
..0..0..0..0..1..1..1....0..0..0..0..1..1..1....0..0..0..0..0..0..0
..0..0..0..0..1..1..1....0..0..1..1..1..1..1....0..0..0..0..0..0..1
..0..0..0..0..1..1..1....0..0..1..1..1..1..1....0..0..0..0..0..0..1
..0..0..0..1..1..1..1....1..1..1..1..1..1..1....0..0..0..0..0..1..1
..0..0..0..0..1..1..1....0..1..1..1..1..1..1....0..0..0..1..1..1..1

Links

Crossrefs

Cf. A202335.

Formula

Empirical: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (167/720)*n^5 + (265/144)*n^4 + (5999/720)*n^3 + (974/45)*n^2 + (4191/140)*n + 19.
Conjectures from Colin Barker, May 28 2018: (Start)
G.f.: x*(81 - 378*x + 854*x^2 - 1148*x^3 + 966*x^4 - 502*x^5 + 148*x^6 - 19*x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A202334 Number of (n+1) X 8 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

Original entry on oeis.org

100, 368, 1112, 2906, 6800, 14588, 29174, 55057, 98958, 170614, 283766, 457370, 717062, 1096910, 1641488, 2408309, 3470656, 4920852, 6874012, 9472322, 12889892, 17338232, 23072402, 30397889, 39678266, 51343690, 65900298, 83940562
Offset: 1

Views

Author

R. H. Hardin, Dec 17 2011

Keywords

Comments

Column 7 of A202335.

Examples

			Some solutions for n=5:
  0 0 0 0 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 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 1    0 0 0 0 0 1 1 1    0 0 0 0 0 0 1 1
  0 0 0 0 0 0 1 1    0 0 0 0 0 1 1 1    0 0 1 1 1 1 1 1
  0 0 1 1 1 1 1 1    1 1 1 1 1 1 1 1    1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1    0 0 1 1 1 1 1 1    1 1 1 1 1 1 1 1

Links

Crossrefs

Cf. A202335.

Formula

Empirical: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (67/1440)*n^6 + (59/120)*n^5 + (8927/2880)*n^4 + (1439/120)*n^3 + (140383/5040)*n^2 + (1243/35)*n + 21.
Conjectures from Colin Barker, May 28 2018: (Start)
G.f.: x*(100 - 532*x + 1400*x^2 - 2254*x^3 + 2366*x^4 - 1636*x^5 + 722*x^6 - 185*x^7 + 21*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
Showing 1-6 of 6 results.

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