A259166 Positive heptagonal numbers (A000566) that are hexagonal numbers (A000384) divided by 2.
189, 393298308, 817809556618215, 1700522115268371779430, 3536001066647854270462804353, 7352626249945315029422809413582264, 15288771624335254149144023973574781130123, 31790890742313650111822470662710981230881538170
Offset: 1
Examples
189 is in the sequence because 189 is the 9th heptagonal number, and 2*189 is the 14th hexagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..158
- Index entries for linear recurrences with constant coefficients, signature (2079363,-2079363,1).
Programs
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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
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Mathematica
LinearRecurrence[{2079363, -2079363, 1},{189, 393298308, 817809556618215}, 20] (* Vincenzo Librandi, Jun 20 2015 *) -
PARI
Vec(-9*x*(2*x^2+33189*x+21)/((x-1)*(x^2-2079362*x+1)) + O(x^20))
Formula
G.f.: -9*x*(2*x^2+33189*x+21) / ((x-1)*(x^2-2079362*x+1)).
Comments