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A126528 Number of base 7 n-digit numbers with adjacent digits differing by five or less. 14
1, 7, 47, 317, 2137, 14407, 97127, 654797, 4414417, 29760487, 200635007, 1352612477, 9118849897, 61476161767, 414451220087, 2794088129357, 18836784876577, 126991149906247, 856130823820367, 5771740692453437, 38911098273822457, 262325293105201927 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

PROG

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))

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

CROSSREFS

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

Sequence in context: A163346 A186446 A244830 * A214992 A241364 A098405

Adjacent sequences:  A126525 A126526 A126527 * A126529 A126530 A126531

KEYWORD

nonn,base

AUTHOR

R. H. Hardin, Dec 28 2006

STATUS

approved

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Last modified March 1 08:23 EST 2021. Contains 341732 sequences. (Running on oeis4.)