OFFSET
0,2
COMMENTS
Partial sums of A038165.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 20.
Index entries for linear recurrences with constant coefficients, signature (6,-10,-10,50,-34,-66,110,0,-110,66,34,-50,10,10,-6,1).
FORMULA
a(n)= sum(A060098(n+5, 5)).
G.f.: 1/((1-x^2)^5*(1-x)^6) = 1/((1-x)^11*(1+x)^5).
a(n) = (14175*(30827+1941*(-1)^n) + 1440*(676427+11445*(-1)^n)*n + 126*(6861329+27375*(-1)^n)*n^2 + 1600*(258451+189*(-1)^n)*n^3 + 10*(12016607+945*(-1)^n)*n^4 + 22444800*n^5 + 2754192*n^6 + 220800*n^7 + 11130*n^8 + 320*n^9 + 4*n^10)/ 464486400. - Colin Barker, Jan 17 2017
MATHEMATICA
Accumulate[CoefficientList[Series[1/((1-x)(1-x^2))^5, {x, 0, 35}], x]] (* or *) LinearRecurrence[ {6, -10, -10, 50, -34, -66, 110, 0, -110, 66, 34, -50, 10, 10, -6, 1}, {1, 6, 26, 86, 246, 622, 1442, 3102, 6292, 12122, 22374, 39754, 68354, 114114, 185614, 294866}, 30] (* Harvey P. Dale, Mar 06 2016 *)
PROG
(PARI) Vec(1/ ((1-x)^11*(1+x)^5) + O(x^40)) \\ Colin Barker, Jan 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 06 2001
STATUS
approved