|
%I #12 May 05 2023 10:22:23
%S 1,6,26,86,246,622,1442,3102,6292,12122,22374,39754,68354,114114,
%T 185614,294866,458601,699556,1048476,1546116,2246244,3218644,4553484,
%U 6365684,8801104,12042732,16319252,21913612,29174652,38528732,50495236,65702076,84906041
%N Sixth column (m=5) of triangle A060098.
%C Partial sums of A038165.
%H Colin Barker, <a href="/A060101/b060101.txt">Table of n, a(n) for n = 0..1000</a>
%H Jia Huang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Huang/huang8.html">Partially Palindromic Compositions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 20.
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,-10,50,-34,-66,110,0,-110,66,34,-50,10,10,-6,1).
%F a(n)= sum(A060098(n+5, 5)).
%F G.f.: 1/((1-x^2)^5*(1-x)^6) = 1/((1-x)^11*(1+x)^5).
%F 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
%t 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 *)
%o (PARI) Vec(1/ ((1-x)^11*(1+x)^5) + O(x^40)) \\ _Colin Barker_, Jan 17 2017
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 06 2001
|
