A109821 - OEIS

%I #21 Apr 25 2024 14:55:52

%S 27,482,3855,20329,82346,277295,813738,2145712,5192450,11708366,

%T 24881487,50269005,97217758,180966915,325691821,568823951,967074547,

%U 1604701323,2604691419,4143692621,6471712062,9937820779,15023357512,22384420182,32905773076,47768686720

%N Column 11 of array illustrated in A089574 and related to A034261.

%H Georg Fischer, <a href="/A109821/b109821.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F G.f.: 27 + 482*x -x^2*(3855 -29786*x +118759*x^2 -310071*x^3 +574122*x^4 -780978*x^5 +792535*x^6 -601009*x^7 +336759*x^8 -135622*x^9 +37194*x^10 -6228*x^11 +481*x^12) /(x-1)^13. - _R. J. Mathar_, Aug 28 2018

%e An examination of the relevant ordered Gaussian polynomials reveals the following distribution (beginning with partitions of length three):

%e 1 10 15 1

%e 6 52 180 216 28

%e 12 114 530 1386 1547 266

%e 18 168 880 3086 7007 7616 1554

%e therefore (by summing each row) this sequence begins

%e 27

%e 482

%e 3855

%e 20329

%t LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1}, {27,482, 3855,20329,82346,277295,813738,2145712,5192450,11708366,24881487, 50269005, 97217758,180966915,325691821}, 1001] (* _Georg Fischer_, Feb 28 2019 *)

%Y Cf. A034261, A109820.

%Y Cf. A000330 (column 2), A086602 (column 3), A089574 (column 4), A107600 (column 5), A107601 (column 6), A109125 (column 7), A109126 (column 8), A109820 (column 9), A108538 (column 10), A109821 (column 11), A110553 (column 12), A110624 (column 13).

%K nonn

%O 0,1

%A _Alford Arnold_, Jul 18 2005

%E More terms from _R. J. Mathar_, Aug 28 2018