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A157265 a(n) = 36*n^2 - 17*n + 2. 5
21, 112, 275, 510, 817, 1196, 1647, 2170, 2765, 3432, 4171, 4982, 5865, 6820, 7847, 8946, 10117, 11360, 12675, 14062, 15521, 17052, 18655, 20330, 22077, 23896, 25787, 27750, 29785, 31892, 34071, 36322, 38645, 41040, 43507, 46046, 48657, 51340 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)* (1728*n-408)^2=1 can be written as A157267(n)^2-a(n)* A157266(n)^2=1 (see also the second comment in A157267). - Vincenzo Librandi, Jan 27 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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 27 2012

G.f.: x*(21 + 49*x + 2*x^2)/(1-x)^3. - Vincenzo Librandi, Jan 27 2012

E.g.f.: (36*x^2 + 19*x + 2)*exp(x) - 2. - G. C. Greubel, Feb 04 2018

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {21, 112, 275}, 40] (* Vincenzo Librandi, Jan 27 2012 *)

PROG

(PARI) a(n)=36*n^2-17*n+2 \\ Charles R Greathouse IV, Jan 11 2012

(MAGMA) I:=[21, 112, 275]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 2012

CROSSREFS

Cf. A157266, A157267.

Sequence in context: A039456 A182827 A255285 * A275916 A129135 A158091

Adjacent sequences:  A157262 A157263 A157264 * A157266 A157267 A157268

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 26 2009

STATUS

approved

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Last modified August 5 07:25 EDT 2020. Contains 336209 sequences. (Running on oeis4.)