A126369 Number of base 15 n-digit numbers with adjacent digits differing by one or less.

1, 15, 43, 125, 365, 1069, 3137, 9219, 27123, 79869, 235361, 693991, 2047367, 6042659, 17841247, 52694573, 155679885, 460055423, 1359834747, 4020216877, 11887503933, 35156155109, 103985848697, 307611659819, 910083564731

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+7*x-57*x^2+73*x^3+75*x^4-121*x^5-33*x^6+37*x^7+4*x^8) / (1-8*x+20*x^2-8*x^3-30*x^4+24*x^5+12*x^6-8*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: A173873 A124708 A204734 * A193647 A133343 A027845

Adjacent sequences: A126366 A126367 A126368 * A126370 A126371 A126372

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved