login
A126397
Number of base 10 n-digit numbers with adjacent digits differing by two or less.
3
1, 10, 44, 200, 918, 4236, 19598, 90790, 420870, 1951636, 9051480, 41983154, 194736668, 903293618, 4190003458, 19435777562, 90155141564, 418195731384, 1939853565942, 8998257693932, 41739569773726, 193614349514214
OFFSET
0,2
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2.
FORMULA
Conjectures from Colin Barker, May 31 2017: (Start)
G.f.: (1 + 3*x - 15*x^2 + 2*x^3 + x^4) / (1 - 7*x + 11*x^2 - x^4).
a(n) = 7*a(n-1) - 11*a(n-2) + 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]`-$[i+1]`>2)+($[i+1]`-$[i]`>2))
CROSSREFS
Cf. Base 10 differing by one or less A126364.
Sequence in context: A076373 A097215 A281993 * A164607 A200189 A240383
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved