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A126531 Number of base 10 n-digit numbers with adjacent digits differing by five or less. 0
1, 10, 80, 660, 5430, 44692, 367826, 3027314, 24915652, 205062892, 1687725824, 13890462738, 114322452324, 940906242802, 7743925534706, 63734705924048, 524554726284436, 4317234336897124, 35532064407664766, 292438978880594940 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..19.

FORMULA

Conjectures from Colin Barker, May 31 2017: (Start)

G.f.: (1 - x)*(1 + 3*x - x^3) / ((1 + x)*(1 - 9*x + 6*x^2 + 3*x^3 - 2*x^4)).

a(n) = 8*a(n-1) + 3*a(n-2) - 9*a(n-3) - a(n-4) + 2*a(n-5) for n>4.

(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 10 differing by four or less A126505, three or less A126478, two or less A126397, one or less A126364.

Sequence in context: A341917 A037509 A037692 * A200162 A165511 A165750

Adjacent sequences:  A126528 A126529 A126530 * A126532 A126533 A126534

KEYWORD

nonn,base

AUTHOR

R. H. Hardin, Dec 28 2006

STATUS

approved

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Last modified August 17 12:30 EDT 2022. Contains 356189 sequences. (Running on oeis4.)