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A181788 Number of solutions to n^2 = a^2 + b^2 + c^2 with nonnegative a, b, c. 4
1, 3, 3, 6, 3, 9, 6, 9, 3, 15, 9, 12, 6, 15, 9, 24, 3, 18, 15, 18, 9, 36, 12, 21, 6, 27, 15, 42, 9, 27, 24, 27, 3, 51, 18, 39, 15, 33, 18, 54, 9, 36, 36, 36, 12, 69, 21, 39, 6, 51, 27, 69, 15, 45, 42, 54, 9, 81, 27, 48, 24, 51, 27, 117, 3, 63, 51, 54, 18, 96, 39, 57, 15, 60, 33, 102, 18, 90, 54, 63, 9, 123, 36, 66, 36, 78, 36, 114, 12, 72, 69, 93, 21, 126, 39, 84, 6, 78, 51, 168, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Paul D. Hanna and Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: [x^(n^2)] G(x)^3 where G(x) = Sum_{k>=0} x^(k^2); the notation [x^(n^2)] G(x)^3 denotes the coefficient of x^(n^2) in G(x)^3. [From Paul D. Hanna, Apr 20 2012]

MATHEMATICA

nn=100; t=Table[0, {nn}]; Do[n=Sqrt[a^2+b^2+c^2]; If[n<=nn && IntegerQ[n], t[[n]]++], {a, 0, nn}, {b, 0, nn}, {c, 0, nn}]; Prepend[t, 1]

PROG

(PARI) {a(n)=local(G=sum(k=0, n, x^(k^2)+x*O(x^(n^2)))); polcoeff(G^3, n^2)} /* Paul D. Hanna */

(PARI) A(n)=my(G=sum(k=0, n, x^(k^2), x*O(x^(n^2)))^3); vector(n+1, k, polcoeff(G, (k-1)^2)) \\ Charles R Greathouse IV, Apr 20 2012

CROSSREFS

Cf. A016725, A016727, A181786, A181787.

Sequence in context: A260152 A130695 A308083 * A112163 A058587 A196439

Adjacent sequences:  A181785 A181786 A181787 * A181789 A181790 A181791

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 12 2010

STATUS

approved

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Last modified June 14 21:10 EDT 2021. Contains 345040 sequences. (Running on oeis4.)