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 1-10 of 12 results. Next

A250770 Number of (2+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

18, 34, 62, 114, 214, 410, 798, 1570, 3110, 6186, 12334, 24626, 49206, 98362, 196670, 393282, 786502, 1572938, 3145806, 6291538, 12582998, 25165914, 50331742, 100663394, 201326694, 402653290, 805306478, 1610612850, 3221225590
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 2 of A250769.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 12*2^(n-1) + 4*n + 2.
Empirical g.f.: 2*x*(9 - 19*x + 8*x^2) / ((1 - x)^2*(1 - 2*x)). - Colin Barker, Nov 19 2018

A250764 Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

35, 62, 114, 216, 418, 820, 1622, 3224, 6426, 12828, 25630, 51232, 102434, 204836, 409638, 819240, 1638442, 3276844, 6553646, 13107248, 26214450, 52428852, 104857654, 209715256, 419430458, 838860860, 1677721662, 3355443264
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250769.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 25*2^(n-1) + 2*n + 8.
Empirical g.f.: x*(35 - 78*x + 41*x^2) / ((1 - x)^2*(1 - 2*x)). - Colin Barker, Nov 18 2018

A250765 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

68, 114, 196, 350, 648, 1234, 2396, 4710, 9328, 18554, 36996, 73870, 147608, 295074, 589996, 1179830, 2359488, 4718794, 9437396, 18874590, 37748968, 75497714, 150995196, 301990150, 603980048, 1207959834, 2415919396, 4831838510
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A250769.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 36*2^(n-1) + 10*n + 22.
Empirical g.f.: 2*x*(34 - 79*x + 40*x^2) / ((1 - x)^2*(1 - 2*x)). - Colin Barker, Nov 18 2018

A250766 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

133, 214, 344, 572, 996, 1812, 3412, 6580, 12884, 25460, 50580, 100788, 201172, 401908, 803348, 1606196, 3211860, 6423156, 12845716, 25690804, 51380948, 102761204, 205521684, 411042612, 822084436, 1644168052, 3288335252
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250769.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 49*2^(n-1) + 32*n + 52.
Empirical g.f.: x*(133 - 318*x + 153*x^2) / ((1 - x)^2*(1 - 2*x)). - Colin Barker, Nov 18 2018

A250767 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

262, 410, 622, 962, 1558, 2666, 4798, 8978, 17254, 33722, 66574, 132194, 263350, 525578, 1049950, 2098610, 4195846, 8390234, 16778926, 33556226, 67110742, 134219690, 268437502, 536873042, 1073744038, 2147485946, 4294969678
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A250769.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 64*2^(n-1) + 84*n + 114.
Empirical g.f.: 2*x*(131 - 319*x + 146*x^2) / ((1 - x)^2*(1 - 2*x)). - Colin Barker, Nov 18 2018

A250768 Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

519, 798, 1158, 1680, 2526, 4020, 6810, 12192, 22758, 43692, 85362, 168504, 334590, 666564, 1330314, 2657616, 5312022, 10620636, 21237666, 42471528, 84939054, 169873908, 339743418, 679482240, 1358959686, 2717914380, 5435823570
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A250769.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 81*2^(n-1) + 198*n + 240.
Empirical g.f.: 3*x*(173 - 426*x + 187*x^2) / ((1 - x)^2*(1 - 2*x)). - Colin Barker, Nov 19 2018

A250771 Number of (3+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

36, 66, 114, 196, 344, 622, 1158, 2208, 4284, 8410, 16634, 33052, 65856, 131430, 262542, 524728, 1049060, 2097682, 4194882, 8389236, 16777896, 33555166, 67109654, 134218576, 268436364, 536871882, 1073742858, 2147484748, 4294968464
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A250769.

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(n) = 16*2^(n-1) + n^2 + 11*n + 8.
Empirical g.f.: 2*x*(3 - 2*x)*(6 - 15*x + 8*x^2) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 19 2018

A250772 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

72, 130, 216, 350, 572, 962, 1680, 3046, 5700, 10922, 21272, 41870, 82956, 165010, 328992, 656822, 1312340, 2623226, 5244840, 10487902, 20973852, 41945570, 83888816, 167775110, 335547492, 671092042, 1342180920, 2684358446, 5368713260
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 4 of A250769.

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(n) = 20*2^(n-1) + 4*n^2 + 26*n + 22.
Empirical g.f.: 2*x*(36 - 115*x + 107*x^2 - 32*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 19 2018

A250773 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

144, 258, 418, 648, 996, 1558, 2526, 4284, 7600, 14010, 26586, 51472, 100956, 199614, 396598, 790212, 1577064, 3150370, 6296562, 12588504, 25171924, 50338278, 100670478, 201334348, 402661536, 805315338, 1610622346, 3221235744
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 5 of A250769.

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(n) = 24*2^(n-1) + 11*n^2 + 57*n + 52.
Empirical g.f.: 2*x*(72 - 231*x + 212*x^2 - 64*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 19 2018

A250774 Number of (6+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

288, 514, 820, 1234, 1812, 2666, 4020, 6322, 10468, 18250, 33252, 62642, 120756, 236266, 466516, 926194, 1844676, 3680714, 7351812, 14692978, 29374228, 58735594, 117457140, 234898994, 469781412, 939544906, 1879070500, 3758120242
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 6 of A250769.

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(n) = 28*2^(n-1) + 26*n^2 + 120*n + 114.
Empirical g.f.: 2*x*(144 - 463*x + 421*x^2 - 128*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 19 2018
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