login
A126478
Number of base 10 n-digit numbers with adjacent digits differing by three or less.
2
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
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
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 27 2006
STATUS
approved