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 1-5 of 5 results.

A250737 Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

18, 22, 30, 46, 78, 142, 270, 526, 1038, 2062, 4110, 8206, 16398, 32782, 65550, 131086, 262158, 524302, 1048590, 2097166, 4194318, 8388622, 16777230, 33554446, 67108878, 134217742, 268435470, 536870926, 1073741838, 2147483662, 4294967310
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250742.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 2^(n+1) + 14.
Empirical g.f.: 2*x*(9 - 16*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 16 2018

A250738 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

34, 38, 46, 62, 94, 158, 286, 542, 1054, 2078, 4126, 8222, 16414, 32798, 65566, 131102, 262174, 524318, 1048606, 2097182, 4194334, 8388638, 16777246, 33554462, 67108894, 134217758, 268435486, 536870942, 1073741854, 2147483678, 4294967326
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A250742.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 2^(n+1) + 30.
Empirical g.f.: 2*x*(17 - 32*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 17 2018

A250739 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

66, 70, 78, 94, 126, 190, 318, 574, 1086, 2110, 4158, 8254, 16446, 32830, 65598, 131134, 262206, 524350, 1048638, 2097214, 4194366, 8388670, 16777278, 33554494, 67108926, 134217790, 268435518, 536870974, 1073741886, 2147483710, 4294967358
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250742.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 2^(n+1) + 62.
Empirical g.f.: 2*x*(33 - 64*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 17 2018

A250740 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

130, 134, 142, 158, 190, 254, 382, 638, 1150, 2174, 4222, 8318, 16510, 32894, 65662, 131198, 262270, 524414, 1048702, 2097278, 4194430, 8388734, 16777342, 33554558, 67108990, 134217854, 268435582, 536871038, 1073741950, 2147483774, 4294967422
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A250742.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 2^(n+1) + 126.
Empirical g.f.: 2*x*(65 - 128*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 17 2018

A250741 Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

258, 262, 270, 286, 318, 382, 510, 766, 1278, 2302, 4350, 8446, 16638, 33022, 65790, 131326, 262398, 524542, 1048830, 2097406, 4194558, 8388862, 16777470, 33554686, 67109118, 134217982, 268435710, 536871166, 1073742078, 2147483902, 4294967550, 8589934846, 17179869438
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A250742.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 2^(n+1) + 254.
Empirical g.f.: 2*x*(129 - 256*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 17 2018
Showing 1-5 of 5 results.

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