A126397 Number of base 10 n-digit numbers with adjacent digits differing by two or less.

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.

Links

Table of n, a(n) for n=0..21.

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

Adjacent sequences: A126394 A126395 A126396 * A126398 A126399 A126400

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved