A157433 128n^2 + 2336n + 10657.

13121, 15841, 18817, 22049, 25537, 29281, 33281, 37537, 42049, 46817, 51841, 57121, 62657, 68449, 74497, 80801, 87361, 94177, 101249, 108577, 116161, 124001, 132097, 140449, 149057, 157921, 167041, 176417, 186049, 195937, 206081, 216481

Offset

1,1

Comments

The identity (128*n^2+2336*n+10657)^2-(4*n^2+73*n+333)*( 64*n+584)^2=1 can be written as a(n)^2-A157431(n)* A157432(n)^2=1.

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

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

G.f.: x*(-10657*x^2-23522*x-13121)/(x-1)^3

Mathematica

LinearRecurrence[{3, -3, 1}, {13121, 15841, 18817}, 50]

Prog

(Magma) I:=[13121, 15841, 18817]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n)=128*n^2+2336*n+10657 \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Sequence in context: A233689 A250904 A250948 * A089212 A023320 A206149

Adjacent sequences: A157430 A157431 A157432 * A157434 A157435 A157436

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 01 2009

Status

approved