A156841 529n^2 - 312n + 46.

46, 263, 1538, 3871, 7262, 11711, 17218, 23783, 31406, 40087, 49826, 60623, 72478, 85391, 99362, 114391, 130478, 147623, 165826, 185087, 205406, 226783, 249218, 272711, 297262, 322871, 349538, 377263, 406046, 435887, 466786, 498743, 531758

Offset

0,1

Comments

The identity (279841*n^2-165048*n+24335)^2-(529*n^2-312*n+46)*(12167*n-3588)^2=1 can be written as A156843(n)^2-a(n)*A156846(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).

Formula

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

G.f.: (46+125*x+887*x^2)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {46, 263, 1538}, 40]

Prog

(Magma) I:=[46, 263, 1538]; [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)=529*n^2-312*n+46 \\ Charles R Greathouse IV, Dec 23 2011

Crossrefs

Cf. A156843, A156846, A156849.

Sequence in context: A251403 A026913 A244744 * A086979 A289274 A296402

Adjacent sequences: A156838 A156839 A156840 * A156842 A156843 A156844

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010

Status

approved