A126505 Number of base 10 n-digit numbers with adjacent digits differing by four or less.

1, 10, 70, 510, 3720, 27142, 198034, 1444904, 10542368, 76919662, 561224422, 4094828862, 29876859864, 217988781808, 1590498774316, 11604663002012, 84670422615182, 617775842744470, 4507441679052256, 32887382581680414

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

Links

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

Formula

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

G.f.: (1 + 3*x - 3*x^2 - 4*x^3 + x^4 + x^5) / (1 - 7*x - 3*x^2 + 6*x^3 + x^4 - x^5).

a(n) = 7*a(n-1) + 3*a(n-2) - 6*a(n-3) - a(n-4) + a(n-5) for n>5.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))

Crossrefs

Base 10 differing by three or less A126478, two or less A126397, one or less A126364.

Sequence in context: A257114 A037600 A037705 * A038779 A246427 A172499

Adjacent sequences: A126502 A126503 A126504 * A126506 A126507 A126508

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved