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 1-3 of 3 results.

A126476 Number of base 8 n-digit numbers with adjacent digits differing by three or less.

Original entry on oeis.org

1, 8, 44, 252, 1446, 8300, 47642, 273466, 1569700, 9010108, 51718192, 296863410, 1704001644, 9781001986, 56143138234, 322262685896, 1849793972828, 10617852738356, 60946677537854, 349835093256180, 2008060117756986
Offset: 0

Views

Author

R. H. Hardin, Dec 27 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3.

Crossrefs

Cf. Base 8 differing by two or less A126395, one or less A126362.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 - x)*(1 + 3*x - x^3) / (1 - 6*x + x^2 + 3*x^3 - x^4).
a(n) = 6*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) for n>4.
(End)

A126503 Number of base 8 n-digit numbers with adjacent digits differing by four or less.

Original entry on oeis.org

1, 8, 52, 348, 2322, 15500, 103462, 690610, 4609826, 30770620, 205394096, 1371006978, 9151480836, 61086196378, 407750773322, 2721739165358, 18167627307952, 121269034961780, 809471627267722, 5403228578160660
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

Crossrefs

Cf. Base 8 differing by three or less A126476, two or less A126395, one or less A126362.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + 2*x - x^2 - x^3) / (1 - 6*x - 5*x^2 + 3*x^3 + 2*x^4).
a(n) = 6*a(n-1) + 5*a(n-2) - 3*a(n-3) - 2*a(n-4) for n>3.
(End)

A126529 Number of base 8 n-digit numbers with adjacent digits differing by five or less.

Original entry on oeis.org

1, 8, 58, 426, 3124, 22914, 168066, 1232708, 9041498, 66316346, 486408084, 3567639634, 26167436306, 191929340708, 1407737135338, 10325278224266, 75732441613044, 555471977422754, 4074200053901346, 29882886543125508
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.

Crossrefs

Cf. Base 8 differing by four or less A126503, three or less A126476, two or less A126395, one or less A126362.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + x - x^2) / (1 - 7*x - 3*x^2 + 4*x^3).
a(n) = 7*a(n-1) + 3*a(n-2) - 4*a(n-3) for n>2.
(End)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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