A126531 Number of base 10 n-digit numbers with adjacent digits differing by five or less.

1, 10, 80, 660, 5430, 44692, 367826, 3027314, 24915652, 205062892, 1687725824, 13890462738, 114322452324, 940906242802, 7743925534706, 63734705924048, 524554726284436, 4317234336897124, 35532064407664766, 292438978880594940

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: A369474 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