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A060100 Fifth column (m=4) of triangle A060098. 2

%I #11 May 05 2023 10:22:41

%S 1,5,19,55,140,316,660,1284,2370,4170,7062,11550,18348,28380,42900,

%T 63492,92235,131703,185185,256685,351208,474760,634712,839800,1100580,

%U 1429428,1841100,2352732,2984520,3759720,4705464,5852760,7237461,8900265,10887855

%N Fifth column (m=4) of triangle A060098.

%C Partial sums of A038164.

%H Colin Barker, <a href="/A060100/b060100.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_13">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,-10,29,-9,-36,36,9,-29,10,6,-5,1).

%F a(n)= sum(A060098(n+4, 4)).

%F G.f.: 1/((1-x^2)^4*(1-x)^5) = 1/((1-x)^9*(1+x)^4).

%F a(n) = (315*(3797+299*(-1)^n) + 12*(204347+4165*(-1)^n)*n + 2*(970241+4095*(-1)^n)*n^2 + 28*(28457+15*(-1)^n)*n^3 + 189168*n^4 + 26936*n^5 + 2268*n^6 + 104*n^7 + 2*n^8) / 1290240. - _Colin Barker_, Jan 17 2017

%o (PARI) Vec(1 / ((1-x)^9*(1+x)^4) + O(x^40)) \\ _Colin Barker_, Jan 17 2017

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Apr 06 2001

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Last modified June 18 20:01 EDT 2024. Contains 373486 sequences. (Running on oeis4.)