A126539 Number of base 18 n-digit numbers with adjacent digits differing by five or less.

1, 18, 168, 1628, 15938, 156652, 1541646, 15178334, 149460562, 1471805948, 14493780280, 142729983350, 1405560587628, 13841533266014, 136307239633698, 1342312628779666, 13218690669418640, 130173687322873468

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..17.

Formula

G.f.: (1+6*x-33*x^2-51*x^3+76*x^4+64*x^5-36*x^6-20*x^7) / (1-12*x+15*x^2+67*x^3-52*x^4-72*x^5+28*x^6+20*x^7) (conjectured). - Colin Barker, Jul 18 2017

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 18 differing by four or less A126513, three or less A126486, two or less A126405, one or less A126372.

Sequence in context: A327792 A071539 A125381 * A213802 A161499 A162346

Adjacent sequences: A126536 A126537 A126538 * A126540 A126541 A126542

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved