A259210 - OEIS

%I #9 Aug 16 2015 12:04:01

%S 15,567645,21362755051,803965923024825,30256453525753512135,

%T 1138671371184241752666901,42852758352891300594112643235,

%U 1612720706714039835374593462842225,60693131033623416811596149786491655551,2284125291706662961573569665690233502167245

%N Positive hexagonal numbers (A000384) that are other hexagonal numbers divided by 3.

%H Colin Barker, <a href="/A259210/b259210.txt">Table of n, a(n) for n = 1..219</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (37635,-37635,1).

%F a(n) = 37635*a(n-1)-37635*a(n-2)+a(n-3).

%F G.f.: -x*(x^2+3120*x+15) / ((x-1)*(x^2-37634*x+1)).

%e 15 is in the sequence because 15 is the 3rd hexagonal number, and 3*15 is the 5th hexagonal number.

%o (PARI) Vec(-x*(x^2+3120*x+15)/((x-1)*(x^2-37634*x+1)) + O(x^20))

%Y Cf. A000384, A076139, A121338, A259211.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jun 21 2015