A154277 a(n) = 81*n^2 - 72*n + 17.

17, 26, 197, 530, 1025, 1682, 2501, 3482, 4625, 5930, 7397, 9026, 10817, 12770, 14885, 17162, 19601, 22202, 24965, 27890, 30977, 34226, 37637, 41210, 44945, 48842, 52901, 57122, 61505, 66050, 70757, 75626, 80657, 85850, 91205, 96722

Offset: 0

Author

Vincenzo Librandi, Jan 06 2009

Keywords

• nonn
• easy

Comments

The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as a(n+1)^2 - A154254(n+1)*A154267(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A154254, A154267.

Programs

Magma

I:=[26, 197, 530]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 02 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {26, 197, 530}, 40] (* Vincenzo Librandi, Feb 02 2012 *)
Table[81n^2-72n+17,{n,0,40}] (* Harvey P. Dale, Oct 16 2022 *)

PARI

for(n=0, 22, print1(81*n^2 - 72*n + 17", ")); \\ Vincenzo Librandi, Feb 02 2012

Formula

G.f.: (17 - 25*x + 170*x^2)/(1-x)^3. - Vincenzo Librandi, Feb 02 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 02 2012

a(n) = A017221(n-1)^2 + 1 with A017221(-1) = -4. - Bruno Berselli, Feb 02 2012

E.g.f.: (17 + 9*x + 81*x^2)*exp(x). - G. C. Greubel, Sep 09 2016

Extensions

92205 replaced by 91205 - R. J. Mathar, Jan 07 2009

Edited by Charles R Greathouse IV, Aug 09 2010