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Number of base 12 n-digit numbers with adjacent digits differing by two or less.
3

%I #11 Jul 18 2017 01:46:05

%S 1,12,54,250,1168,5486,25848,122024,576748,2728038,12909648,61108496,

%T 289310874,1369855464,6486547342,30716393200,145458062754,

%U 688830120102,3262050022332,15447978818780,73156731187376,346447866034700

%N Number of base 12 n-digit numbers with adjacent digits differing by two or less.

%C [Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2.

%F G.f.: (1+5*x-22*x^2-17*x^3+21*x^4+7*x^5-4*x^6) / (1-7*x+8*x^2+15*x^3-9*x^4-5*x^5+2*x^6) (conjectured). - _Colin Barker_, Jul 17 2017

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

%Y Cf. Base 12 differing by one or less A126366.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006