A126528 Number of base 7 n-digit numbers with adjacent digits differing by five or less.

1, 7, 47, 317, 2137, 14407, 97127, 654797, 4414417, 29760487, 200635007, 1352612477, 9118849897, 61476161767, 414451220087, 2794088129357, 18836784876577, 126991149906247, 856130823820367, 5771740692453437, 38911098273822457, 262325293105201927

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

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.

For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,6} containing no subwords 00 and 11. - Milan Janjic, Jan 31 2015

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,5).

Crossrefs

Cf. Base 7 differing by four or less A126502, three or less A126475, two or less A126394, one or less A126361.

Programs

Mathematica

LinearRecurrence[{6, 5}, {1, 7}, 25] (* Paolo Xausa, Aug 08 2024 *)

PARI

Vec((1+x)/(1-6*x-5*x^2) + O(x^30)) \\ Colin Barker, Sep 08 2016

Formula

From Philippe Deléham, Mar 24 2012: (Start)

G.f.: (1+x)/(1-6*x-5*x^2).

a(n) = 6*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 7 .

a(n) = Sum_{k=0..=n} A054458(n,k)*4^k.

(End)

a(n) = A091928(n+1)/5. - Philippe Deléham, Mar 27 2012

a(n) = (((3-sqrt(14))^n * (-4+sqrt(14)) + (3+sqrt(14))^n * (4+sqrt(14)))) / (2*sqrt(14)). - Colin Barker, Sep 08 2016