OFFSET
0,11
COMMENTS
Number of partitions of n into parts of size two and five.
It appears that, for n >= 2, a(n-2) is also (1) the number of partitions of 3n that are 6-term arithmetic progressions and (2) floor(n/2) - floor(2n/5). - John W. Layman, Jun 29 2009
REFERENCES
G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004. page 30, Exercise 48.
D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 213
M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 1, 0, -1).
FORMULA
G.f.: 1/((1-x^2)(1-x^5)) = 1/((x-1)^2*(1+x)*(1+x+x^2+x^3+x^4)).
Euler transform of finite sequence [0, 1, 0, 0, 1].
a(n) = -a(-7 - n) = a(n - 10) + 1 = a(n - 2) + a(n - 5) - a(n - 7). - Michael Somos, Jan 25 2005
a(n) = 7/20 + n/10 + (-1)^n/4 + (A105384(n) + 2*(A010891(n) + A105384(n+4)))/5. - R. J. Mathar, Jun 28 2009
a(n) = floor(n/10 + (3 + (-1)^n)/4). - Tani Akinari, Jun 20 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x^2) (1 - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 21 2013 *)
PROG
(PARI) {a(n) = if( n<-6, -a(-7 - n), polcoeff( 1 / (1 - x^2) / (1 - x^5) + x * O(x^n), n))} /* Michael Somos, Jan 25 2005 */
(PARI) a(n) = floor(n/10+(3+(-1)^n)/4) \\ Charles R Greathouse IV, Jun 19 2013
(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^2)*(1-x^5)))); // Wesley Ivan Hurt, Dec 27 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved