A156774 a(n) = 6561*n^2 - 3564*n + 485.

485, 3482, 19601, 48842, 91205, 146690, 215297, 297026, 391877, 499850, 620945, 755162, 902501, 1062962, 1236545, 1423250, 1623077, 1836026, 2062097, 2301290, 2553605, 2819042, 3097601, 3389282, 3694085, 4012010, 4343057, 4687226

Offset: 0

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Comments

The identity (6561*n^2 - 3564*n + 485)^2 - (81*n^2 - 44*n + 6)*(729*n - 198)^2 = 1 can be written as a(n)^2 - A156676(n)*A156772(n)^2 = 1 for n>0.

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. A156676, A156772.

Programs

Magma

I:=[485, 3482, 19601]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

Mathematica

LinearRecurrence[{3,-3,1},{485,3482,19601},40]
Table[6561n^2-3564n+485,{n,0,30}] (* Harvey P. Dale, Dec 09 2020 *)

PARI

a(n)= 6561*n^2-3564*n+485 \\ Charles R Greathouse IV, Dec 23 2011

Sage

[485 -3564*n +6561*n^2 for n in (0..40)] # G. C. Greubel, Jun 21 2021

Formula

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

G.f.: (485 + 2027*x + 10610*x^2)/(1-x)^3.

E.g.f.: (485 + 2997*x + 6561*x^2)*exp(x). - G. C. Greubel, Jun 21 2021

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010