A259167 Positive octagonal numbers (A000567) that are squares (A000290) divided by 2.

8, 78408, 752875208, 7229107670408, 69413891098384008, 666512175097575576008, 6399849835873029582446408, 61451357457540654953074835208, 590055927907455532986394985222408, 5665716958316030570194709695030728008, 54402213643694597627554069505290065112008

Offset

1,1

Comments

Intersection of A000567 and A001105. - Michel Marcus, Jun 20 2015

Links

Colin Barker, Table of n, a(n) for n = 1..251

Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).

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

Cf. A000290, A000567, A001105, A259156-A259166.

Sequence in context: A137142 A368066 A036535 * A048565 A339777 A269877

Adjacent sequences: A259164 A259165 A259166 * A259168 A259169 A259170

Keyword

nonn,easy

Author

Colin Barker, Jun 19 2015

Status

approved