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%I A126528 #34 Aug 08 2024 16:18:45
%S A126528 1,7,47,317,2137,14407,97127,654797,4414417,29760487,200635007,
%T A126528 1352612477,9118849897,61476161767,414451220087,2794088129357,
%U A126528 18836784876577,126991149906247,856130823820367,5771740692453437,38911098273822457,262325293105201927
%N A126528 Number of base 7 n-digit numbers with adjacent digits differing by five or less.
%C A126528 [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.
%C A126528 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
%H A126528 Colin Barker, <a href="/A126528/b126528.txt">Table of n, a(n) for n = 0..1000</a>
%H A126528 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,5).
%F A126528 From _Philippe Deléham_, Mar 24 2012: (Start)
%F A126528 G.f.: (1+x)/(1-6*x-5*x^2).
%F A126528 a(n) = 6*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 7 .
%F A126528 a(n) = Sum_{k=0..=n} A054458(n,k)*4^k.
%F A126528 (End)
%F A126528 a(n) = A091928(n+1)/5. - _Philippe Deléham_, Mar 27 2012
%F A126528 a(n) = (((3-sqrt(14))^n * (-4+sqrt(14)) + (3+sqrt(14))^n * (4+sqrt(14)))) / (2*sqrt(14)). - _Colin Barker_, Sep 08 2016
%t A126528 LinearRecurrence[{6, 5}, {1, 7}, 25] (* _Paolo Xausa_, Aug 08 2024 *)
%o A126528 (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))
%o A126528 (PARI) Vec((1+x)/(1-6*x-5*x^2) + O(x^30)) \\ _Colin Barker_, Sep 08 2016
%Y A126528 Cf. Base 7 differing by four or less A126502, three or less A126475, two or less A126394, one or less A126361.
%K A126528 nonn,base
%O A126528 0,2
%A A126528 _R. H. Hardin_, Dec 28 2006

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