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A259167
Positive octagonal numbers (A000567) that are squares (A000290) divided by 2.
12
8, 78408, 752875208, 7229107670408, 69413891098384008, 666512175097575576008, 6399849835873029582446408, 61451357457540654953074835208, 590055927907455532986394985222408, 5665716958316030570194709695030728008, 54402213643694597627554069505290065112008
OFFSET
1,1
COMMENTS
Intersection of A000567 and A001105. - Michel Marcus, Jun 20 2015
FORMULA
G.f.: -8*x*(x^2+198*x+1) / ((x-1)*(x^2-9602*x+1)).
EXAMPLE
8 is in the sequence because 8 is the 2nd octagonal number, and 2*8 is the 4th square.
MATHEMATICA
LinearRecurrence[{9603, -9603, 1}, {8, 78408, 752875208}, 20] (* Vincenzo Librandi, Jun 20 2015 *)
PROG
(PARI) Vec(-8*x*(x^2+198*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 19 2015
STATUS
approved