A126476 -id:A126476 - cp's OEIS frontend

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

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

Offset: 0

R. H. Hardin, Dec 28 2006

[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.

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

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

R. H. Hardin, Dec 28 2006

[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.

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

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)

cp's OEIS Frontend

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

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