%I #6 Jun 13 2015 00:55:23

%S 1,1891,26335,71156485,991081981,2677903145191,37298379237211,

%T 100780206894952201,1403687203222107385,3792762303606727977835,

%U 52826364168762410080471,142736816433155393822880781,1988067387723517337746328821,5371757345852607787523567324911

%N Hexagonal numbers (A000384) which are also centered triangular numbers (A005448).

%H Colin Barker, <a href="/A254285/b254285.txt">Table of n, a(n) for n = 1..437</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,37634,-37634,-1,1).

%F a(n) = a(n-1)+37634*a(n-2)-37634*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+1890*x^3-13190*x^2+1890*x+1) / ((x-1)*(x^2-194*x+1)*(x^2+194*x+1)).

%e 1891 is in the sequence because it is the 31st hexagonal number and the 36th centered triangular number.

%o (PARI) Vec(-x*(x^4+1890*x^3-13190*x^2+1890*x+1)/((x-1)*(x^2-194*x+1)*(x^2+194*x+1)) + O(x^100))

%Y Cf. A000384, A005448, A254283, A254284.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 28 2015