OFFSET
0,5
COMMENTS
The number of partitions of 2*(n-3) into at most 6 parts. - Colin Barker, Mar 31 2015
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,0,-3,1,1,0,0,1,1,-3,0,0,2,-1).
FORMULA
G.f.: x^3*(x^4+x^3+x^2+1) / ((x-1)^6*(x+1)*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).
a(n) = 2*a(n-1) - 3*a(n-4) + a(n-5) + a(n-6) + a(n-9) + a(n-10) - 3*a(n-11) + 2*a(n-14) - a(n-15). - Wesley Ivan Hurt, Jul 28 2022
EXAMPLE
For n=4 the 2 partitions of 2*4 = 8 are [1,1,1,1,1,3] and [1,1,1,1,2,2].
MATHEMATICA
CoefficientList[Series[x^3 (x^4 + x^3 + x^2 + 1) / ((x - 1)^6 (x + 1) (x^2 + x + 1)^2 (x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 22 2015 *)
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=2*n, k++, , [6, 6]); k))
(PARI) concat([0, 0, 0], Vec(x^3*(x^4+x^3+x^2+1)/((x-1)^6*(x+1)*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 22 2015
STATUS
approved