A126478 Number of base 10 n-digit numbers with adjacent digits differing by three or less.

1, 10, 58, 350, 2130, 12990, 79258, 483646, 2951370, 18010366, 109906170, 670689902, 4092809194, 24975905246, 152412637946, 930080892110, 5675713495690, 34635399953406, 211358612597658, 1289792038765742

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3

Links

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

Formula

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

G.f.: (1 + 3*x - 8*x^2 - 6*x^3 + 6*x^4) / (1 - 7*x + 4*x^2 + 10*x^3 - 6*x^4).

a(n) = 7*a(n-1) - 4*a(n-2) - 10*a(n-3) + 6*a(n-4) for n>4.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))

Crossrefs

Cf. Base 10 differing by two or less A126397, one or less A126364.

Sequence in context: A125320 A321112 A126730 * A223470 A044148 A044529

Adjacent sequences: A126475 A126476 A126477 * A126479 A126480 A126481

Keyword

nonn,base

Author

R. H. Hardin, Dec 27 2006

Status

approved