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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
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
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
MATHEMATICA
LinearRecurrence[{6, 5}, {1, 7}, 25] (* Paolo Xausa, Aug 08 2024 *)
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
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved