A260937 Indices i of pentagonal numbers P(i) such that (P(i)-1)/2 is also a pentagonal number.

1, 106, 345, 122130, 397937, 140937722, 459218761, 162642008866, 529938052065, 187688737293450, 611548052864057, 216592640194632242, 705725923067069521, 249947719095868313626, 814407103671345362985, 288439451243991839291970

Offset: 1

Author

Ray Chandler, Aug 04 2015

Keywords

• nonn
• easy

Comments

Companion sequence to A174685.

Links

• Ray Chandler, Table of n, a(n) for n = 1..653 (terms to 1000 digits)
• Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Crossrefs

Cf. A000326, A174685.

Programs

Magma

I:=[1,106,345,122130,397937]; [n le 5 select I[n] else Self(n-1)+1154*Self(n-2)-1154*Self(n-3)-Self(n-4)+Self(n-5): n in [1..30]]; // Vincenzo Librandi, Aug 05 2015

Mathematica

LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 106, 345, 122130, 397937}, 20] (* Vincenzo Librandi, Aug 05 2015 *)

Formula

G.f.: x*(1 + 105*x - 915*x^2 + 615*x^3 + 2*x^4)/((1 - x)*(1 - 34*x + x^2)*(1 + 34*x + x^2)). [Bruno Berselli, Aug 05 2015]