A154377 a(n) = 25*n^2 + 2*n.

27, 104, 231, 408, 635, 912, 1239, 1616, 2043, 2520, 3047, 3624, 4251, 4928, 5655, 6432, 7259, 8136, 9063, 10040, 11067, 12144, 13271, 14448, 15675, 16952, 18279, 19656, 21083, 22560, 24087, 25664, 27291, 28968, 30695, 32472, 34299, 36176

Offset: 1

Author

Vincenzo Librandi, Jan 08 2009

Keywords

• nonn
• easy

Comments

The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - a(n)*A154379(n)^2 = 1 (see also the second comment in A154375). - Vincenzo Librandi, Jan 30 2012

The continued fraction expansion of sqrt(4*a(n)) is [10n; {2, 1, 1, 5n-1, 1, 1, 2, 20n}]. - Magus K. Chu, Sep 27 2022

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A154375, A154379.

Programs

Mathematica

LinearRecurrence[{3,-3,1},{27,104,231},50]

PARI

a(n)=25*n^2+2*n \\ Charles R Greathouse IV, Dec 23 2011

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(27 + 23*x)/(1-x)^3.

E.g.f.: (25*x^2 + 27*x)*exp(x). - G. C. Greubel, Sep 15 2016