A259157 - OEIS

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

%S 3,3570,4119885,4754343828,5486508657735,6331426236682470,

%T 7306460390622912753,8431648959352604634600,9730115592632515125415755,

%U 11228544962248963102125146778,12957731156319710787337293966165,14953210525847983999624135111807740

%N Positive triangular numbers (A000217) that are hexagonal numbers (A000384) divided by 2.

%C Intersection of A000217 and A033991 (even hexagonal numbers divided by 2). - _Michel Marcus_, Jun 20 2015

%H Colin Barker, <a href="/A259157/b259157.txt">Table of n, a(n) for n = 1..327</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1155,-1155,1).

%F G.f.: -3*x*(35*x+1) / ((x-1)*(x^2-1154*x+1)).

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

%t LinearRecurrence[{1155, -1155, 1}, {3, 3570, 4119885}, 20] (* _Vincenzo Librandi_, Jun 20 2015 *)

%o (PARI) Vec(-3*x*(35*x+1)/((x-1)*(x^2-1154*x+1)) + O(x^20))

%Y Cf. A000217, A000384, A033991, A259156, A259158-A259167.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jun 19 2015