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 1-7 of 7 results.

A250521 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

222, 1180, 5029, 18859, 65310, 214812, 682921, 2122743, 6501118, 19720580, 59462069, 178644459, 535616774, 1604254580, 4803055177, 14379531399, 43056528118, 128955131820, 386326404261, 1157662173067, 3469836562702
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Examples

			Some solutions for n=5:
..2..2..0....2..2..1....1..1..0....2..0..0....2..1..1....2..1..0....2..0..0
..1..2..0....1..1..0....2..2..2....2..0..0....1..0..0....2..2..1....2..1..1
..1..2..0....2..2..1....1..1..1....2..0..1....2..1..1....1..1..0....1..0..0
..1..2..0....0..0..1....1..1..1....2..1..2....2..1..1....0..1..0....0..0..0
..1..2..0....1..1..2....0..0..0....1..0..2....1..0..0....0..1..0....0..0..0
..0..1..2....0..0..1....1..1..1....0..0..2....1..0..2....0..1..2....1..2..2

Links

Crossrefs

Column 2 of A250527.

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
Empirical g.f.: x*(222 - 1928*x + 7379*x^2 - 16515*x^3 + 23687*x^4 - 22151*x^5 + 13066*x^6 - 4404*x^7 + 648*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 14 2018

A250522 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

867, 5029, 21955, 82023, 279161, 896191, 2771901, 8374485, 24944039, 73714737, 217061167, 638657339, 1880873517, 5549684027, 16412416857, 48651910233, 144539853387, 430255351197, 1282888681851, 3830445412591, 11449627377217
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250527.

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
Empirical g.f.: x*(867 - 7109*x + 25244*x^2 - 52780*x^3 + 72501*x^4 - 66849*x^5 + 39534*x^6 - 13260*x^7 + 1944*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 14 2018

A250523 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

3123, 18859, 82023, 300131, 993123, 3088923, 9240559, 26984403, 77707851, 222271083, 634724183, 1815888579, 5216209523, 15062616251, 43743061503, 127741126963, 374944674139, 1105460634123, 3271582279911, 9712201092643
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Examples

			Some solutions for n=3:
..2..2..1..1..0....0..1..1..0..0....2..0..0..0..0....2..1..2..1..1
..1..1..1..1..0....1..2..2..2..2....1..0..0..1..2....1..0..1..0..0
..0..0..1..2..1....0..1..1..1..1....1..0..0..1..2....0..0..1..0..0
..0..0..1..2..1....0..1..2..2..2....1..0..0..1..2....0..0..1..0..2

Links

Crossrefs

Column 4 of A250527.

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
Empirical g.f.: x*(3123 - 24863*x + 83452*x^2 - 163338*x^3 + 214295*x^4 - 196963*x^5 + 119218*x^6 - 39828*x^7 + 5832*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 14 2018

A250524 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

10660, 65310, 279161, 993123, 3183434, 9580060, 27710543, 78195145, 217483704, 600720730, 1657359573, 4587075263, 12774934710, 35868804392, 101626338475, 290581221893, 838071567940, 2435917896966, 7127659997521, 20972608975899
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250527.

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
Empirical g.f.: x*(10660 - 83930*x + 270921*x^2 - 497821*x^3 + 618997*x^4 - 570765*x^5 + 360190*x^6 - 119532*x^7 + 17496*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 14 2018

A250525 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

35064, 214812, 896191, 3088923, 9580060, 27910024, 78204775, 213775147, 575554760, 1537251580, 4096973351, 10948193747, 29449843532, 79976028008, 219684249567, 610918710611, 1719898743144, 4898224161036, 14095078529871
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Comments

Column 6 of A250527

Examples

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

Links

Formula

Empirical: a(n) = 14*a(n-1) -85*a(n-2) +294*a(n-3) -639*a(n-4) +906*a(n-5) -839*a(n-6) +490*a(n-7) -164*a(n-8) +24*a(n-9)

A250526 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

112373, 682921, 2771901, 9240559, 27710543, 78204775, 212707851, 565044857, 1478308633, 3832617341, 9897332961, 25578008747, 66435440107, 174080131035, 461563409759, 1240974976389, 3386986664197, 9384561755841, 26376931311941
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Comments

Column 7 of A250527

Examples

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

Links

Formula

Empirical: a(n) = 14*a(n-1) -85*a(n-2) +294*a(n-3) -639*a(n-4) +906*a(n-5) -839*a(n-6) +490*a(n-7) -164*a(n-8) +24*a(n-9)

A250520 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

50, 1180, 21955, 300131, 3183434, 27910024, 212707851, 1462376991, 9314700106, 56025183452, 322542598187
Offset: 1

Views

Author

R. H. Hardin, Nov 24 2014

Keywords

Comments

Diagonal of A250527

Examples

			Some solutions for n=3
..2..1..2..1....1..1..0..0....2..2..1..1....2..1..2..0....2..0..1..0
..1..0..1..0....0..0..0..0....1..1..0..0....2..1..2..1....2..1..2..2
..1..1..2..1....1..1..2..2....2..2..1..1....1..1..2..2....2..1..2..2
..0..0..2..1....0..1..2..2....0..2..1..2....0..1..2..2....0..1..2..2
Showing 1-7 of 7 results.

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