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 14 results. Next

A250748 Number of (n+1)X(n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

32, 237, 1353, 6663, 29814, 124785, 497471, 1911819, 7141428, 26081157, 93524517, 330341391, 1152105314, 3974940633, 13587035451, 46067386899, 155081690112, 518770438893, 1725559820033, 5710472045463, 18811007467662, 61706609086017
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Comments

Diagonal of A250755

Examples

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

Links

A250749 Number of (n+1) X (2+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

72, 237, 756, 2361, 7272, 22197, 67356, 203601, 613872, 1847757, 5555556, 16691241, 50122872, 150466917, 451597356, 1355185281, 4066342272, 12200599677, 36604944756, 109821125721, 329475960072, 988453046037, 2965409469756
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A250755.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (63*3^n - 24*2^n + 3)/2.
Empirical g.f.: 3*x*(24 - 65*x + 42*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

A250750 Number of (n+1) X (3+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

129, 423, 1353, 4239, 13089, 40023, 121593, 367839, 1109649, 3341223, 10048233, 30193839, 90679809, 272236023, 817101273, 2452090239, 7357843569, 22076676423, 66236320713, 198721545039, 596189800929, 1788619734423, 5365959866553
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250755.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (114*3^n -48*2^n + 12)/2.
Empirical g.f.: 3*x*(43 - 117*x + 78*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

A250751 Number of (n+1) X (4+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

203, 663, 2123, 6663, 20603, 63063, 191723, 580263, 1751003, 5273463, 15861323, 47665863, 143161403, 429811863, 1290090923, 3871583463, 11617371803, 34857358263, 104582560523, 313768653063, 941347902203, 2824127592663
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A250755.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (180*3^n - 80*2^n + 26)/2.
Empirical g.f.: x*(7 - 9*x)*(29 - 42*x) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

A250752 Number of (n+1) X (5+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

294, 957, 3066, 9633, 29814, 91317, 277746, 840873, 2537934, 7644477, 22994826, 69107313, 207567654, 623194437, 1870566306, 5613664953, 16844926974, 50542645197, 151643664186, 454962449793, 1364950263894, 4094976620757
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250755.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (261*3^n - 120*2^n + 45)/2.
Empirical g.f.: 3*x*(98 - 269*x + 186*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

A250753 Number of (n+1) X (6+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

402, 1305, 4182, 13149, 40722, 124785, 379662, 1149669, 3470442, 10454265, 31448742, 94518189, 283898562, 852383745, 2558527422, 7678334709, 23040509082, 69132537225, 207419631702, 622302935229, 1866996886002, 5601166818705
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A250755.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (357*3^n - 168*2^n + 69)/2.
Empirical g.f.: 3*x*(134 - 369*x + 258*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

A250754 Number of (n+1) X (7+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

527, 1707, 5471, 17211, 53327, 163467, 497471, 1506651, 4548527, 13702827, 41223071, 123898491, 372154127, 1117379787, 3353974271, 10065592731, 30204118127, 90627034347, 271910463071, 815790109371, 2447487768527
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A250755.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (468*3^n - 224*2^n + 98)/2.
Empirical g.f.: x*(527 - 1455*x + 1026*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

A250756 Number of (1+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

32, 72, 129, 203, 294, 402, 527, 669, 828, 1004, 1197, 1407, 1634, 1878, 2139, 2417, 2712, 3024, 3353, 3699, 4062, 4442, 4839, 5253, 5684, 6132, 6597, 7079, 7578, 8094, 8627, 9177, 9744, 10328, 10929, 11547, 12182, 12834, 13503, 14189, 14892, 15612
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 1 of A250755.

Formula

Empirical: a(n) = (17/2)*n^2 + (29/2)*n + 9.
Conjectures from Colin Barker, Nov 17 2018: (Start)
G.f.: x*(32 - 24*x + 9*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250757 Number of (2+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

105, 237, 423, 663, 957, 1305, 1707, 2163, 2673, 3237, 3855, 4527, 5253, 6033, 6867, 7755, 8697, 9693, 10743, 11847, 13005, 14217, 15483, 16803, 18177, 19605, 21087, 22623, 24213, 25857, 27555, 29307, 31113, 32973, 34887, 36855, 38877, 40953, 43083
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 2 of A250755.

Formula

Empirical: a(n) = 27*n^2 + 51*n + 27.
Conjectures from Colin Barker, Nov 18 2018: (Start)
G.f.: 3*x*(35 - 26*x + 9*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250758 Number of (3+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

332, 756, 1353, 2123, 3066, 4182, 5471, 6933, 8568, 10376, 12357, 14511, 16838, 19338, 22011, 24857, 27876, 31068, 34433, 37971, 41682, 45566, 49623, 53853, 58256, 62832, 67581, 72503, 77598, 82866, 88307, 93921, 99708, 105668, 111801, 118107
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A250755.

Formula

Empirical: a(n) = (173/2)*n^2 + (329/2)*n + 81.
Conjectures from Colin Barker, Nov 18 2018: (Start)
G.f.: x*(332 - 240*x + 81*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)
Showing 1-10 of 14 results. Next

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