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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A228460 Number of arrays of maxima of three adjacent elements of some length n+2 0..7 array.

Original entry on oeis.org

8, 64, 372, 1716, 6812, 25096, 92430, 357510, 1453506, 6026658, 24812574, 100499726, 402014614, 1601790692, 6399288759, 25687363699, 103446743321, 416881245069, 1678284756985, 6747301104293, 27104825271091, 108875206199331
Offset: 1

Views

Author

R. H. Hardin Aug 22 2013

Keywords

Comments

Column 7 of A228461

Examples

			Some solutions for n=4
..5....7....3....0....7....6....7....2....7....5....2....4....3....4....7....5
..1....1....2....1....6....1....4....1....3....4....2....2....6....0....1....5
..0....0....1....5....2....2....2....1....6....1....0....2....7....0....2....0
..1....4....2....5....7....6....5....6....6....0....6....6....7....6....5....5

Links

Formula

Empirical: a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -42*a(n-4) +168*a(n-6) -48*a(n-7) +195*a(n-8) +340*a(n-9) +154*a(n-10) +408*a(n-11) +432*a(n-12) +276*a(n-13) +338*a(n-14) +268*a(n-15) +149*a(n-16) +118*a(n-17) +71*a(n-18) +28*a(n-19) +14*a(n-20) +6*a(n-21) +a(n-22)

A228462 Number of arrays of maxima of three adjacent elements of some length 7 0..n array.

Original entry on oeis.org

17, 91, 310, 821, 1847, 3703, 6812, 11721, 19117, 29843, 44914, 65533, 93107, 129263, 175864, 235025, 309129, 400843, 513134, 649285, 812911, 1007975, 1238804, 1510105, 1826981, 2194947, 2619946, 3108365, 3667051, 4303327, 5025008, 5840417
Offset: 1

Views

Author

R. H. Hardin, Aug 22 2013

Keywords

Examples

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

Links

Crossrefs

Row 5 of A228461.

Formula

Empirical: a(n) = (2/15)*n^5 + (7/6)*n^4 + (25/6)*n^3 + (19/3)*n^2 + (21/5)*n + 1.
Conjectures from Colin Barker, Sep 11 2018: (Start)
G.f.: x*(17 - 11*x + 19*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A228463 Number of arrays of maxima of three adjacent elements of some length 8 0..n array.

Original entry on oeis.org

27, 183, 736, 2227, 5615, 12453, 25096, 46941, 82699, 138699, 223224, 346879, 522991, 768041, 1102128, 1549465, 2138907, 2904511, 3886128, 5130027, 6689551, 8625805, 11008376, 13916085, 17437771, 21673107, 26733448, 32742711, 39838287
Offset: 1

Views

Author

R. H. Hardin, Aug 22 2013

Keywords

Examples

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

Links

Crossrefs

Row 6 of A228461.

Formula

Empirical: a(n) = (2/45)*n^6 + (8/15)*n^5 + (115/36)*n^4 + 8*n^3 + (1667/180)*n^2 + (149/30)*n + 1.
Conjectures from Colin Barker, Sep 11 2018: (Start)
G.f.: x*(27 - 6*x + 22*x^2 - 27*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
Previous Showing 11-13 of 13 results.

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