A259210 Positive hexagonal numbers (A000384) that are other hexagonal numbers divided by 3.
15, 567645, 21362755051, 803965923024825, 30256453525753512135, 1138671371184241752666901, 42852758352891300594112643235, 1612720706714039835374593462842225, 60693131033623416811596149786491655551, 2284125291706662961573569665690233502167245
Offset: 1
Examples
15 is in the sequence because 15 is the 3rd hexagonal number, and 3*15 is the 5th hexagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..219
- Index entries for linear recurrences with constant coefficients, signature (37635,-37635,1).
Programs
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PARI
Vec(-x*(x^2+3120*x+15)/((x-1)*(x^2-37634*x+1)) + O(x^20))
Formula
a(n) = 37635*a(n-1)-37635*a(n-2)+a(n-3).
G.f.: -x*(x^2+3120*x+15) / ((x-1)*(x^2-37634*x+1)).