A126392 Number of base 5 n-digit numbers with adjacent digits differing by two or less.

1, 5, 19, 75, 295, 1161, 4569, 17981, 70763, 278483, 1095951, 4313041, 16973681, 66798773, 262882051, 1034554523, 4071419319, 16022795225, 63056626377, 248155086189, 976597549531, 3843333571747, 15125179200799, 59524119253665

Offset

0,2

Comments

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..23.

S. Kitaev, J. Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO]

Index entries for linear recurrences with constant coefficients, signature (4,0,-1).

Formula

a(n) = 4*a(n-1)-a(n-3). G.f.: -(x^2-x-1)/(x^3-4*x+1). [Colin Barker, Nov 25 2012]

Mathematica

LinearRecurrence[{4, 0, -1}, {1, 5, 19}, 30] (* Harvey P. Dale, Apr 27 2018 *)

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 5 differing by one or less A057960.

Sequence in context: A295374 A212403 A098913 * A206373 A149767 A149768

Adjacent sequences: A126389 A126390 A126391 * A126393 A126394 A126395

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010

Status

approved