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A156677 81n^2 - 118n + 43. 5
43, 6, 131, 418, 867, 1478, 2251, 3186, 4283, 5542, 6963, 8546, 10291, 12198, 14267, 16498, 18891, 21446, 24163, 27042, 30083, 33286, 36651, 40178, 43867, 47718, 51731, 55906, 60243, 64742, 69403, 74226, 79211, 84358, 89667, 95138, 100771 (list; graph; refs; listen; history; text; internal format)
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 A156773(n)^2-a(n)*A156771(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.: (-43+123*x-242*x^2)/(x-1)^3.

For n>1: a(n) = A171198(n-2) - A017305(n-2). [From Reinhard Zumkeller, Jul 13 2010]

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {43, 6, 131}, 40]

PROG

(MAGMA) I:=[43, 6, 131]; [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)=81*n^2-118*n+43 \\ Charles R Greathouse IV, Dec 23 2011

CROSSREFS

Cf. A156771, A156773.

Sequence in context: A292996 A107814 A093762 * A097398 A225210 A033363

Adjacent sequences:  A156674 A156675 A156676 * A156678 A156679 A156680

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 15 2009

EXTENSIONS

Edited by Charles R Greathouse IV, Jul 25 2010

STATUS

approved

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Last modified May 9 12:20 EDT 2021. Contains 343740 sequences. (Running on oeis4.)