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

Author

Wolfdieter Lang, Apr 06 2001

Keywords

• nonn
• easy

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).

Programs

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 *)

PARI

Vec(1/ ((1-x)^11*(1+x)^5) + O(x^40)) \\ Colin Barker, Jan 17 2017

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