%I #7 Jun 04 2017 10:13:25
%S 35245,794629045,28238642425,640790268444865,22771697546069605,
%T 516734554053498696685,18363142444517200268785,
%U 416695777857208665553032505,14808074793520787633419991965,336024308655092047765242836700325,11941261129626387046720630977591145
%N Hexagonal numbers (A000384) that are the sum of fourteen consecutive hexagonal numbers.
%H Colin Barker, <a href="/A257724/b257724.txt">Table of n, a(n) for n = 1..337</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,806402,-806402,-1,1).
%F G.f.: -35*x*(35*x^4+8424*x^3-27932146*x^2+22702680*x+1007) / ((x-1)*(x^2-898*x+1)*(x^2+898*x+1)).
%e 35245 is in the sequence because H(133) = 35245 = 1653 + 1770 + 1891 + 2016 + 2145 + 2278 + 2415 + 2556 + 2701 + 2850 + 3003 + 3160 + 3321 + 3486 = H(29)+...+H(42).
%t LinearRecurrence[{1,806402,-806402,-1,1},{35245,794629045,28238642425,640790268444865,22771697546069605},20] (* _Harvey P. Dale_, Jun 04 2017 *)
%o (PARI) Vec(-35*x*(35*x^4+8424*x^3-27932146*x^2+22702680*x+1007)/((x-1)*(x^2-898*x+1)*(x^2+898*x+1)) + O(x^100))
%Y Cf. A257721, A257722, A257723.
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 06 2015