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A085409 Sum of three solutions of the Diophantine equation x^2 - y^2 = z^3. 5
0, 12, 84, 270, 624, 1200, 2052, 3234, 4800, 6804, 9300, 12342, 15984, 20280, 25284, 31050, 37632, 45084, 53460, 62814, 73200, 84672, 97284, 111090, 126144, 142500, 160212, 179334, 199920, 222024, 245700, 271002, 297984, 326700, 357204, 389550 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Parametric representation of the solution is (x, y, z) = (6n^3, 3n^3, 3n^2), thus getting a(n) = 9n^3 + 3n^2.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 9*n^3 + 3*n^2.

From Colin Barker, Oct 25 2019: (Start)

G.f.: 6*x*(2 + 6*x + x^2) /(1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.

(End)

MATHEMATICA

Table[9n^3 + 3n^2, {n, 0, 34}]

PROG

(PARI) concat(0, Vec(6*x*(2 + 6*x + x^2) /(1 - x)^4 + O(x^40))) \\ Colin Barker, Oct 25 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( 6*x*(2 + 6*x + x^2) /(1 - x)^4)); // Marius A. Burtea, Oct 25 2019

CROSSREFS

Cf. A085377.

Sequence in context: A075476 A298977 A213784 * A303916 A111464 A004407

Adjacent sequences:  A085406 A085407 A085408 * A085410 A085411 A085412

KEYWORD

nonn,easy

AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 13 2003

EXTENSIONS

More terms from Robert G. Wilson v, Aug 16 2003

STATUS

approved

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Last modified April 6 08:53 EDT 2020. Contains 333268 sequences. (Running on oeis4.)