A156773 a(n) = 6561*n^2 - 9558*n + 3482.

3482, 485, 10610, 33857, 70226, 119717, 182330, 258065, 346922, 448901, 564002, 692225, 833570, 988037, 1155626, 1336337, 1530170, 1737125, 1957202, 2190401, 2436722, 2696165, 2968730, 3254417, 3553226, 3865157, 4190210, 4528385

Offset: 0

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Comments

The identity (6561*n^2 - 9558*n + 3482)^2 - (81*n^2 - 118*n + 43)*(729*n - 531)^2 = 1 can be written as a(n)^2 - A156677(n)*A156771(n)^2 = 1 for n>0. [rewritten by Bruno Berselli, Jul 21 2011]

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. A156677, A156771.

Programs

Magma

[6561*n^2-9558*n+3482: n in [0..35]];

Mathematica

Table[6561n^2-9558n+3482,{n,0,30}] (* Harvey P. Dale, Apr 06 2011 *)

PARI

a(n)=6561*n^2-9558*n+3482 \\ Charles R Greathouse IV, Dec 23 2011

Sage

[3482 -9558*n +6561*n^2 for n in (0..35)] # G. C. Greubel, Jun 21 2021

Formula

G.f.: (3482 - 9961*x + 19601*x^2)/(1-x)^3. - Colin Barker, Jan 09 2012

E.g.f.: (3482 - 2997*x + 6561*x^2)*exp(x). - G. C. Greubel, Jun 21 2021

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Sep 03 2022

Extensions

Checked by Michael B. Porter, Jun 16 2010

Offset corrected by N. J. A. Sloane, Jun 22 2010