A131721 Overlay of Pell companion numbers: a(n) = A001333(n) + A001333(n-6).

1, 1, 3, 7, 17, 41, 100, 240, 580, 1400, 3380, 8160, 19700, 47560, 114820, 277200, 669220, 1615640, 3900500, 9416640, 22733780, 54884200, 132502180, 319888560, 772279300, 1864447160, 4501173620, 10866794400, 26234762420, 63336319240

Offset: 0

Author

Paul Curtz, Sep 15 2007

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1).

Crossrefs

Cf. A131710.

Programs

Mathematica

LinearRecurrence[{2, 1}, {1, 1, 3, 7, 17, 41, 100, 240}, 50] (* Paolo Xausa, Mar 01 2024 *)

Formula

a(n) = A001333(n), n<6. a(n) = A001333(n)+A001333(n-6) = 20*A000129(n-3), n>=6.

O.g.f.: (x-1)(x^2+1)(x^4-x^2+1)/(-1+2x+x^2). - R. J. Mathar, Jul 16 2008

For n>5, a(n) = 100*A000129(n+1) -240*A000129(n). - R. J. Mathar, Feb 05 2024

Extensions

Edited and extended by R. J. Mathar, Jul 16 2008