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A126476
Number of base 8 n-digit numbers with adjacent digits differing by three or less.
2
1, 8, 44, 252, 1446, 8300, 47642, 273466, 1569700, 9010108, 51718192, 296863410, 1704001644, 9781001986, 56143138234, 322262685896, 1849793972828, 10617852738356, 60946677537854, 349835093256180, 2008060117756986
OFFSET
0,2
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3.
FORMULA
Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 - x)*(1 + 3*x - x^3) / (1 - 6*x + x^2 + 3*x^3 - x^4).
a(n) = 6*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) for n>4.
(End)
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))
CROSSREFS
Cf. Base 8 differing by two or less A126395, one or less A126362.
Sequence in context: A322498 A147828 A155604 * A220629 A377159 A210118
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 27 2006
STATUS
approved