A258730 -id:A258730 - cp's OEIS frontend

A258736 Number of length n+6 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

16384, 43681, 68120, 98676, 149960, 228081, 331584, 465580, 635992, 849708, 1114752, 1440474, 1837760, 2319263, 2899656, 3595908, 4427584, 5417170, 6590424, 7976754, 9609624, 11526989, 13771760, 16392300, 19442952, 22984600, 27085264

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Row 6 of A258730.

			Some solutions for n=4:
..2....1....1....2....0....0....2....1....3....0....2....1....0....3....0....0
..2....0....1....0....0....0....0....1....3....1....1....1....2....3....0....0
..0....1....2....0....2....2....0....0....2....0....1....2....3....0....2....3
..0....1....0....0....2....2....0....1....2....0....3....0....3....0....2....0
..2....1....0....0....2....0....0....2....2....3....3....2....1....0....0....0
..2....2....0....1....2....0....2....2....2....3....1....2....1....0....0....1
..3....3....2....2....2....0....0....3....0....0....1....2....1....1....0....3
..1....3....1....2....0....0....1....3....2....0....1....0....2....3....1....3
..3....3....1....3....2....1....2....1....2....3....3....0....3....1....2....0
..3....2....1....0....3....0....2....1....3....3....1....0....2....1....3....0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A258730.

Empirical: a(n) = (1/5040)*n^7 + (1/72)*n^6 + (149/360)*n^5 + (239/36)*n^4 + (297247/720)*n^3 + (187297/72)*n^2 + (178036/35)*n + 2212 for n>4.

Empirical g.f.: x*(16384 - 87391*x + 177424*x^2 - 140720*x^3 - 31344*x^4 + 116775*x^5 - 39024*x^6 - 13988*x^7 - 31192*x^8 + 58867*x^9 - 31680*x^10 + 5890*x^11) / (1 - x)^8. - Colin Barker, Jan 26 2018

A258737 Number of length n+7 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

65536, 163020, 220854, 281136, 370510, 526672, 752180, 1038256, 1394568, 1831920, 2362442, 2999800, 3759427, 4658776, 5717596, 6958232, 8405950, 10089288, 12040434, 14295632, 16895617, 19886080, 23318164, 27248992, 31742228, 36868672

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Row 7 of A258730.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A258730.

Empirical: a(n) = (1/5040)*n^7 + (11/720)*n^6 + (361/720)*n^5 + (1285/144)*n^4 + (40822/45)*n^3 + (1121411/180)*n^2 + (480457/35)*n + 7848 for n>5.

Empirical g.f.: x*(65536 - 361268*x + 751702*x^2 - 591152*x^3 - 236266*x^4 + 807960*x^5 - 664864*x^6 + 371040*x^7 - 206700*x^8 + 10940*x^9 + 117664*x^10 - 82072*x^11 + 17481*x^12) / (1 - x)^8. - Colin Barker, Jan 26 2018

cp's OEIS Frontend

A258736 Number of length n+6 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

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