OFFSET
0,2
COMMENTS
a(n) is the number of weak compositions of n with exactly 5 parts equal to 0. - Milan Janjic, Jun 27 2010
Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)^6; see A291000. - Clark Kimberling, Aug 24 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Robert Davis, Greg Simay, Further Combinatorics and Applications of Two-Toned Tilings, arXiv:2001.11089 [math.CO], 2020.
Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.
Index entries for linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64).
FORMULA
G.f.: ((1-x)/(1-2*x))^6.
For n > 0, a(n) = 2^(n-9)*(n+7)*(n^4 + 38*n^3 + 419*n^2 + 1342*n + 1080)/15. - Bruno Berselli, Aug 07 2011
MAPLE
seq(coeff(series(((1-x)/(1-2*x))^6, x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 16 2018
MATHEMATICA
CoefficientList[Series[((1 - x)/(1 - 2 x))^6, {x, 0, 27}], x] (* Michael De Vlieger, Oct 15 2018 *)
PROG
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(((1-x)/(1-2*x))^6)); // G. C. Greubel, Oct 16 2018
(PARI) x='x+O('x^30); Vec(((1-x)/(1-2*x))^6) \\ G. C. Greubel, Oct 16 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 15 2010
STATUS
approved