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A126477
Number of base 9 n-digit numbers with adjacent digits differing by three or less.
2
1, 9, 51, 301, 1787, 10619, 63111, 375091, 2229307, 13249619, 78747531, 468026571, 2781660187, 16532466059, 98258743211, 583989138891, 3470869901227, 20628701920939, 122604233247851, 728683659684651
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 + 2*x - 6*x^2 + 2*x^4) / ((1 - x)*(1 - 6*x + 2*x^3)).
a(n) = 7*a(n-1) - 6*a(n-2) - 2*a(n-3) + 2*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 9 differing by two or less A126396, one or less A126363.
Sequence in context: A080621 A027218 A155617 * A275861 A210054 A272393
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 27 2006
STATUS
approved