A060101 Sixth column (m=5) of triangle A060098.

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

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

Sequence in context: A316160 A224035 A172207 * A036422 A166214 A032169

Adjacent sequences: A060098 A060099 A060100 * A060102 A060103 A060104

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 06 2001

Status

approved