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

A250805 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

36, 379, 3081, 20631, 120304, 634509, 3104985, 14345803, 63351756, 269772537, 1114996177, 4494912111, 17741279760, 68762781541, 262334037201, 987009622419, 3668074098940, 13482629809713, 49069419165081, 176992814380663
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Comments

Diagonal of A250812

Examples

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

Links

A250806 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

100, 379, 1315, 4321, 13735, 42769, 131455, 400681, 1214695, 3669409, 11058895, 33278041, 100036855, 300516049, 902359135, 2708699401, 8129342215, 24394514689, 73196520175, 219615512761, 658898442775, 1976799137329
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A250812.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (126*3^n - 99*2^n + 20)/2.
Empirical g.f.: x*(100 - 221*x + 141*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

A250807 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

225, 873, 3081, 10233, 32745, 102393, 315561, 963513, 2924265, 8840313, 26656041, 80238393, 241255785, 724848633, 2176708521, 6534450873, 19612003305, 58853311353, 176594537001, 529852816953, 1589696862825, 4769367412473
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250812.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (304*3^n - 264*2^n + 66)/2.
Empirical g.f.: 3*x*(75 - 159*x + 106*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

A250808 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

441, 1731, 6171, 20631, 66291, 207831, 641571, 1961031, 5955891, 18013431, 54331971, 163579431, 491905491, 1478051031, 4438822371, 13325805831, 39996095091, 120025640631, 360151632771, 1080604320231, 3242111804691
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A250812.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (620*3^n - 570*2^n + 162)/2.
Empirical g.f.: 3*x*(147 - 305*x + 212*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

A250809 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

784, 3097, 11116, 37333, 120304, 377857, 1167796, 3572173, 10854424, 32839417, 99070876, 298318213, 897166144, 2695921777, 8096612356, 24307531453, 72957983464, 218944728937, 656975744236, 1971210347893, 5914197274384
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250812.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (1131*3^n - 1080*2^n + 335)/2.
Empirical g.f.: x*(784 - 1607*x + 1158*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

A250810 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

1296, 5139, 18537, 62469, 201741, 634509, 1962717, 6007149, 18260061, 55258029, 166730397, 502104429, 1510140381, 4538075949, 13629538077, 40919235309, 122818948701, 368579332269, 1105982969757, 3318438855789, 9956296461021
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A250812.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (1904*3^n - 1869*2^n + 618)/2.
Empirical g.f.: 3*x*(432 - 879*x + 653*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

A250811 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

2025, 8049, 29145, 98481, 318585, 1003089, 3104985, 9507441, 28908345, 87498129, 264041625, 795220401, 2391853305, 7187945169, 21588607065, 64815365361, 194545185465, 583833736209, 1751897569305, 5256485430321, 15771041736825
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A250812.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (3016*3^n - 3024*2^n + 1050)/2.
Empirical g.f.: 3*x*(675 - 1367*x + 1042*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

A250813 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, 11025, 14400, 18496, 23409, 29241, 36100, 44100, 53361, 64009, 76176, 90000, 105625, 123201, 142884, 164836, 189225, 216225, 246016, 278784, 314721, 354025, 396900, 443556, 494209
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 1 of A250812.

Formula

Empirical: a(n) = (1/4)*n^4 + (5/2)*n^3 + (37/4)*n^2 + 15*n + 9.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(36 - 80*x + 85*x^2 - 44*x^3 + 9*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) for n>5.
(End)

A250814 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

129, 379, 873, 1731, 3097, 5139, 8049, 12043, 17361, 24267, 33049, 44019, 57513, 73891, 93537, 116859, 144289, 176283, 213321, 255907, 304569, 359859, 422353, 492651, 571377, 659179, 756729, 864723, 983881, 1114947, 1258689, 1415899
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 2 of A250812.

Formula

Empirical: a(n) = 1*n^4 + 10*n^3 + 37*n^2 + 54*n + 27.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(129 - 266*x + 268*x^2 - 134*x^3 + 27*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) for n>5.
(End)

A250815 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 min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

432, 1315, 3081, 6171, 11116, 18537, 29145, 43741, 63216, 88551, 120817, 161175, 210876, 271261, 343761, 429897, 531280, 649611, 786681, 944371, 1124652, 1329585, 1561321, 1822101, 2114256, 2440207, 2802465, 3203631, 3646396, 4133541, 4667937
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A250812.

Formula

Empirical: a(n) = (15/4)*n^4 + 36*n^3 + (527/4)*n^2 + (359/2)*n + 81.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(432 - 845*x + 826*x^2 - 404*x^3 + 81*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) for n>5.
(End)
Showing 1-10 of 14 results. Next

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