A259167 Positive octagonal numbers (A000567) that are squares (A000290) divided by 2.
8, 78408, 752875208, 7229107670408, 69413891098384008, 666512175097575576008, 6399849835873029582446408, 61451357457540654953074835208, 590055927907455532986394985222408, 5665716958316030570194709695030728008, 54402213643694597627554069505290065112008
Offset: 1
Examples
8 is in the sequence because 8 is the 2nd octagonal number, and 2*8 is the 4th square.
Links
- Colin Barker, Table of n, a(n) for n = 1..251
- Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).
Programs
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Magma
I:=[8, 78408, 752875208]; [n le 3 select I[n] else 9603*Self(n-1)-9603*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 20 2015
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Mathematica
LinearRecurrence[{9603, -9603, 1}, {8, 78408, 752875208}, 20] (* Vincenzo Librandi, Jun 20 2015 *) -
PARI
Vec(-8*x*(x^2+198*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))
Formula
G.f.: -8*x*(x^2+198*x+1) / ((x-1)*(x^2-9602*x+1)).
Comments