A259162 - OEIS

%I #11 Aug 16 2015 12:04:01

%S 6,58311,559902916,5376187741821,51622154137063026,

%T 495675918647891434531,4759480119234899417304336,

%U 45700527609217585557064800441,438816461344227137284036796530846,4213515616126741362983735763224383551,40458176507232509223142693514443734326556

%N Positive hexagonal numbers (A000384) that are pentagonal numbers (A000326) divided by 2.

%C Intersection of A000384 and A193866 (even pentagonal numbers divided by 2). - _Michel Marcus_, Jun 20 2015

%H Colin Barker, <a href="/A259162/b259162.txt">Table of n, a(n) for n = 1..251</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9603,-9603,1).

%F G.f.: -x*(x^2+693*x+6) / ((x-1)*(x^2-9602*x+1)).

%e 6 is in the sequence because 6 is the 2nd hexagonal number, and 2*6 is the 3rd pentagonal number.

%t LinearRecurrence[{9603, -9603, 1}, {6, 58311, 559902916}, 20] (* _Vincenzo Librandi_, Jun 20 2015 *)

%o (PARI) Vec(-x*(x^2+693*x+6)/((x-1)*(x^2-9602*x+1)) + O(x^20))

%Y Cf. A000326, A000384, A193866, A259156-A259161, A259163-A259167.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jun 19 2015