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

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

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

• 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).

Crossrefs

Cf. Base 5 differing by one or less A057960.

Programs

Mathematica

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

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]

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010