%I #34 Aug 08 2024 16:18:45

%S 1,7,47,317,2137,14407,97127,654797,4414417,29760487,200635007,

%T 1352612477,9118849897,61476161767,414451220087,2794088129357,

%U 18836784876577,126991149906247,856130823820367,5771740692453437,38911098273822457,262325293105201927

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

%C [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 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 Colin Barker, <a href="/A126528/b126528.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,5).

%F From _Philippe Deléham_, Mar 24 2012: (Start)

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

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

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

%F (End)

%F a(n) = A091928(n+1)/5. - _Philippe Deléham_, Mar 27 2012

%F 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 LinearRecurrence[{6, 5}, {1, 7}, 25] (* _Paolo Xausa_, Aug 08 2024 *)

%o (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 (PARI) Vec((1+x)/(1-6*x-5*x^2) + O(x^30)) \\ _Colin Barker_, Sep 08 2016

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

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006