A259166 - OEIS

%I #12 Sep 08 2022 08:46:13

%S 189,393298308,817809556618215,1700522115268371779430,

%T 3536001066647854270462804353,7352626249945315029422809413582264,

%U 15288771624335254149144023973574781130123,31790890742313650111822470662710981230881538170

%N Positive heptagonal numbers (A000566) that are hexagonal numbers (A000384) divided by 2.

%C Intersection of A000566 and A033991 (even hexagonal numbers divided by 2). - _Michel Marcus_, Jun 20 2015

%H Colin Barker, <a href="/A259166/b259166.txt">Table of n, a(n) for n = 1..158</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2079363,-2079363,1).

%F G.f.: -9*x*(2*x^2+33189*x+21) / ((x-1)*(x^2-2079362*x+1)).

%e 189 is in the sequence because 189 is the 9th heptagonal number, and 2*189 is the 14th hexagonal number.

%t LinearRecurrence[{2079363, -2079363, 1},{189, 393298308, 817809556618215}, 20] (* _Vincenzo Librandi_, Jun 20 2015 *)

%o (PARI) Vec(-9*x*(2*x^2+33189*x+21)/((x-1)*(x^2-2079362*x+1)) + O(x^20))

%o (Magma) I:=[189,393298308,817809556618215]; [n le 3 select I[n] else 2079363*Self(n-1)-2079363*Self(n-2)+Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 20 2015

%Y Cf. A000384, A000566, A259156-A259165, A259167.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jun 19 2015