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A060101 Sixth column (m=5) of triangle A060098. 2
1, 6, 26, 86, 246, 622, 1442, 3102, 6292, 12122, 22374, 39754, 68354, 114114, 185614, 294866, 458601, 699556, 1048476, 1546116, 2246244, 3218644, 4553484, 6365684, 8801104, 12042732, 16319252, 21913612, 29174652, 38528732, 50495236, 65702076, 84906041 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Partial sums of A038165.
LINKS
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
Sequence in context: A316160 A224035 A172207 * A036422 A166214 A032169
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 06 2001
STATUS
approved

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Last modified May 21 00:01 EDT 2024. Contains 372720 sequences. (Running on oeis4.)