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A156640 169n^2 + 140n + 29. 5
29, 338, 985, 1970, 3293, 4954, 6953, 9290, 11965, 14978, 18329, 22018, 26045, 30410, 35113, 40154, 45533, 51250, 57305, 63698, 70429, 77498, 84905, 92650, 100733, 109154, 117913, 127010, 136445, 146218, 156329, 166778 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (57122*n^2+47320*n+9801)^2-(169*n^2+140*n+29)*(4394*n+1820)^2=1 can be written as A156735(n)^2-a(n)*A156636(n)^2=1.

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) for n>2.

G.f.: (29 + 251*x + 58*x^2)/(1 - x)^3. - Vincenzo Librandi, May 03 2014

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {29, 338, 985}, 50]

CoefficientList[Series[(29 + 251 x + 58 x^2)/(1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, May 03 2014 *)

PROG

(MAGMA) I:=[29, 338, 985]; [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)=169*n^2+140*n+29 \\ Charles R Greathouse IV, Dec 23 2011

CROSSREFS

Cf. A156636, A156718, A156735.

Sequence in context: A057131 A160442 A125417 * A239743 A022689 A234810

Adjacent sequences:  A156637 A156638 A156639 * A156641 A156642 A156643

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 January 22 10:48 EST 2021. Contains 340362 sequences. (Running on oeis4.)