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Search: a126503 -id:a126503
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Number of base 8 n-digit numbers with adjacent digits differing by five or less.
+10
0
1, 8, 58, 426, 3124, 22914, 168066, 1232708, 9041498, 66316346, 486408084, 3567639634, 26167436306, 191929340708, 1407737135338, 10325278224266, 75732441613044, 555471977422754, 4074200053901346, 29882886543125508
OFFSET
0,2
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.
FORMULA
Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + x - x^2) / (1 - 7*x - 3*x^2 + 4*x^3).
a(n) = 7*a(n-1) + 3*a(n-2) - 4*a(n-3) for n>2.
(End)
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))
CROSSREFS
Cf. Base 8 differing by four or less A126503, three or less A126476, two or less A126395, one or less A126362.
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved

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