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

1,2

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).

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]

Mathematica

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

Prog

See A174685 for PARI program attributed to Jack Brennen.
(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

Crossrefs

Cf. A000326, A174685.

Sequence in context: A255818 A090775 A213458 * A200868 A234421 A234414

Adjacent sequences: A260934 A260935 A260936 * A260938 A260939 A260940

Keyword

nonn,easy

Author

Ray Chandler, Aug 04 2015

Status

approved