A099242 (6n+5)-th terms of expansion of 1/(1 - x - x^6).

1, 7, 34, 153, 686, 3088, 13917, 62721, 282646, 1273690, 5739647, 25864698, 116554700, 525233175, 2366870474, 10665883415, 48063918336, 216591552484, 976031547888, 4398313653120, 19820223058176, 89316331907533

Offset: 0

Author

Paul Barry, Oct 08 2004

Keywords

• easy
• nonn

Comments

A row of A099239.

Equals INVERT transform of A000389, C(n,5). [Gary W. Adamson, Feb 02 2009]

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
• Index entries for linear recurrences with constant coefficients, signature (7,-15,20,-15,6,-1).

Crossrefs

Cf. A000389.

Programs

Mathematica

CoefficientList[Series[1/((1 - x)^6 - x), {x, 0, 50}], x] (* G. C. Greubel, Nov 24 2017 *)
LinearRecurrence[{7,-15,20,-15,6,-1},{1,7,34,153,686,3088},30] (* Harvey P. Dale, May 06 2018 *)

PARI

my(x='x+O('x^50)); Vec(1/((1-x)^6-x)) \\ G. C. Greubel, Nov 24 2017

Formula

G.f.: 1/((1-x)^6-x).

a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

a(n) = Sum_{k=0..n} binomial(6*n-5*(k-1), k).

a(n) = Sum_{k=0..n} binomial(n+5*(k+1), k+5*(k+1)).

a(n) = Sum_{k=0..n} binomial(n+5*(k+1), n-k).