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.

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A255113 Number of length n+6 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

2187, 5157, 7498, 10125, 14001, 19263, 25578, 33063, 41851, 52092, 63954, 77624, 93309, 111237, 131658, 154845, 181095, 210730, 244098, 281574, 323561, 370491, 422826, 481059, 545715, 617352, 696562, 783972, 880245, 986081, 1102218, 1229433
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2015

Keywords

Comments

Row 6 of A255107.

Examples

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

Links

Crossrefs

Cf. A255107.

Formula

Empirical: a(n) = (1/120)*n^5 + (3/8)*n^4 + (149/24)*n^3 + (2521/8)*n^2 + (56417/60)*n + 385 for n>4.
Empirical g.f.: x*(2187 - 7965*x + 9361*x^2 - 1248*x^3 - 4614*x^4 + 1405*x^5 + 1230*x^6 + 564*x^7 - 1354*x^8 + 435*x^9) / (1 - x)^6. - Colin Barker, Jan 24 2018

A255114 Number of length n+7 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

6561, 14849, 19338, 23463, 29147, 38010, 49611, 63075, 78552, 96210, 116236, 138837, 164241, 192698, 224481, 259887, 299238, 342882, 391194, 444577, 503463, 568314, 639623, 717915, 803748, 897714, 1000440, 1112589, 1234861, 1367994
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2015

Keywords

Comments

Row 7 of A255107.

Examples

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

Links

Crossrefs

Cf. A255107.

Formula

Empirical: a(n) = (1/120)*n^5 + (5/12)*n^4 + (187/24)*n^3 + (7393/12)*n^2 + (20667/10)*n + 1143 for n>5.
Empirical g.f.: x*(6561 - 24517*x + 28659*x^2 - 1050*x^3 - 20126*x^4 + 11682*x^5 - 2967*x^6 + 3385*x^7 - 168*x^8 - 2466*x^9 + 1008*x^10) / (1 - x)^6. - Colin Barker, Jan 24 2018
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