A126411 - OEIS

%I #10 Sep 25 2015 08:24:51

%S 1,24,114,550,2668,12986,63348,309524,1514230,7415030,36339360,

%T 178207260,874402930,4292397700,21079558088,103555346934,508877542076,

%U 2501307731338,12297585994658,60472695897300,297423291148782

%N Number of base 24 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

%H Alois P. Heinz, <a href="/A126411/b126411.txt">Table of n, a(n) for n = 0..1000</a>

%F 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 b:= proc(n, i) option remember; `if`(n=0, 1, add(

%p      `if`(i=0 or abs(i-j)<3, b(n-1, j), 0), j=1..24))

%p     end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 25 2015

%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 24 differing by one or less A126378.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006