A126373 Number of base 19 n-digit numbers with adjacent digits differing by one or less.

1, 19, 55, 161, 473, 1393, 4109, 12135, 35871, 106113, 314093, 930187, 2755955, 8168423, 24218539, 71826449, 213075513, 632242305, 1876395357, 5569898331, 16536545331, 49103259773, 145827049265, 433134662087, 1286649627671

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+3^(n-1) for base>=n; a(base,n)=a(base-1,n)+3^(n-1)-2 when base=n-1.

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: (1+9*x-100*x^2+236*x^3-7*x^4-469*x^5+216*x^6+290*x^7-111*x^8-53*x^9+6*x^10) / ((1-2*x-x^2)*(1-8*x+20*x^2-8*x^3-31*x^4+28*x^5+10*x^6-12*x^7+x^8)) (conjectured). - Colin Barker, Jul 18 2017

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>1)+($[i+1]`-$[i]`>1))

Crossrefs

Sequence in context: A044502 A069131 A124712 * A125818 A362298 A367518

Adjacent sequences: A126370 A126371 A126372 * A126374 A126375 A126376

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved