A157367 a(n) = 4802*n^2 + 196*n + 1.

4999, 19601, 43807, 77617, 121031, 174049, 236671, 308897, 390727, 482161, 583199, 693841, 814087, 943937, 1083391, 1232449, 1391111, 1559377, 1737247, 1924721, 2121799, 2328481, 2544767, 2770657, 3006151, 3251249, 3505951

Offset

1,1

Comments

The identity (4802*n^2+196*n+1)^2-(49*n^2+2*n)*(686*n+14)^2=1 can be written as a(n)^2-A157365(n)*A157366(n)^2=1.

This formula is the case s=7 of the identity (2*s^4*n^2+4*s^2*n+1)^2-(s^2*n^2+2*n)*(2*s^3*n+2*s)^2=1. - Bruno Berselli, Feb 11 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f: x*(4999 + 4604*x + x^2)/(1-x)^3.

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

E.g.f.: (1 + 4998*x + 4802*x^2)*exp(x) - 1. - G. C. Greubel, Feb 02 2018

Example

For n=1, a(1)=4999; n=2, a(2)=19601; n=3, a(3)=43807

Mathematica

LinearRecurrence[{3, -3, 1}, {4999, 19601, 43807}, 50]

Prog

(Magma) I:=[4999, 19601, 43807]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 4802*n^2+196*n+1.

Crossrefs

Cf. A157365, A157366.

Sequence in context: A031840 A059667 A106767 * A200910 A035901 A203919

Adjacent sequences: A157364 A157365 A157366 * A157368 A157369 A157370

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved