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A157786 a(n) = 27225*n^2 - 15248*n + 2135. 3
14112, 80539, 201416, 376743, 606520, 890747, 1229424, 1622551, 2070128, 2572155, 3128632, 3739559, 4404936, 5124763, 5899040, 6727767, 7610944, 8548571, 9540648, 10587175, 11688152, 12843579, 14053456, 15317783, 16636560, 18009787, 19437464, 20919591 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (1482401250*n^2-830253600*n +116250751)^2-(27225*n^2-15248*n +2135) *(8984250*n -2515920)^2=1 can be written as A157788(n)^2-a(n)*A157787(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*(-14112-38203*x-2135*x^2)/(x-1)^3.

MATHEMATICA

Table[27225*n^2-15248*n+2135, {n, 50}] (* Harvey P. Dale, Nov 26 2010 *)

PROG

(Magma) I:=[14112, 80539, 201416]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];

(PARI) a(n) = 27225*n^2-15248*n+2135.

CROSSREFS

Cf. A157787, A157788.

Sequence in context: A237153 A066698 A035918 * A186834 A263911 A215019

Adjacent sequences: A157783 A157784 A157785 * A157787 A157788 A157789

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 06 2009

EXTENSIONS

More terms from Harvey P. Dale, Nov 26 2010

STATUS

approved

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Last modified December 3 09:39 EST 2022. Contains 358517 sequences. (Running on oeis4.)