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

0,1

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).

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

Mathematica

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

Prog

(Magma) [6561*n^2-9558*n+3482: n in [0..35]];
(PARI) a(n)=6561*n^2-9558*n+3482 \\ Charles R Greathouse IV, Dec 23 2011
(SageMath) [3482 -9558*n +6561*n^2 for n in (0..35)] # G. C. Greubel, Jun 21 2021

Crossrefs

Cf. A156677, A156771.

Sequence in context: A328817 A159215 A176380 * A174753 A031557 A031737

Adjacent sequences: A156770 A156771 A156772 * A156774 A156775 A156776

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 15 2009

Extensions

Checked by Michael B. Porter, Jun 16 2010

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

Status

approved