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A126411 Number of base 24 n-digit numbers with adjacent digits differing by two or less.

%I A126411 #10 Sep 25 2015 08:24:51
%S A126411 1,24,114,550,2668,12986,63348,309524,1514230,7415030,36339360,
%T A126411 178207260,874402930,4292397700,21079558088,103555346934,508877542076,
%U A126411 2501307731338,12297585994658,60472695897300,297423291148782
%N A126411 Number of base 24 n-digit numbers with adjacent digits differing by two or less.
%C A126411 [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
%H A126411 Alois P. Heinz, <a href="/A126411/b126411.txt">Table of n, a(n) for n = 0..1000</a>
%F A126411 G.f.: -(8*x^12 +49*x^11 -117*x^10 -525*x^9 +450*x^8 +1346*x^7 -678*x^6 -1203*x^5 +458*x^4 +302*x^3 -145*x^2 +11*x +1) / (2*x^12 +11*x^11 -33*x^10 -115*x^9 +150*x^8 +286*x^7 -260*x^6 -237*x^5 +190*x^4 +38*x^3 -53*x^2 +13*x -1). - _Alois P. Heinz_, Sep 25 2015
%p A126411 b:= proc(n, i) option remember; `if`(n=0, 1, add(
%p A126411      `if`(i=0 or abs(i-j)<3, b(n-1, j), 0), j=1..24))
%p A126411     end:
%p A126411 a:= n-> b(n, 0):
%p A126411 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 25 2015
%o A126411 (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 A126411 Cf. Base 24 differing by one or less A126378.
%K A126411 nonn,base
%O A126411 0,2
%A A126411 _R. H. Hardin_, Dec 28 2006