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A276285
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Number of ways of writing n as a sum of 13 squares.
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6
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1, 26, 312, 2288, 11466, 41808, 116688, 265408, 535704, 1031914, 1899664, 3214224, 5043376, 7801744, 12066912, 17689152, 24443978, 34039200, 48210760, 64966096, 83323344, 109157152, 145532816, 185245632, 227110416, 284788010, 363737712
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OFFSET
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0,2
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COMMENTS
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More generally, the ordinary generating function for the number of ways of writing n as a sum of k squares is theta_3(0, q)^k = 1 + 2*k*q + 2*(k - 1)*k*q^2 + (4/3)*(k - 2)*(k - 1)*k*q^3 + (2/3)*((k - 3)*(k - 2)*(k - 1) + 3)*k*q^4 + (4/15) *(k - 1)*k*(k^3 - 9*k^2 + 26*k - 9)*q^5 + ..., where theta is the Jacobi theta functions.
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LINKS
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FORMULA
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G.f.: theta_3(0,q)^13, where theta_3(x,q) is the third Jacobi theta function.
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MATHEMATICA
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Table[SquaresR[13, n], {n, 0, 26}]
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CROSSREFS
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Cf. Number of ways of writing n as a sum of k squares: A004018 (k = 2), A005875 (k = 3), A000118 (k = 4), A000132 (k = 5), A000141 (k = 6), A008451 (k = 7), A000143 (k = 8), A008452 (k = 9), A000144 (k = 10), A008453 (k = 11), A000145 (k = 12), this sequence (k = 13), A000152 (k = 16).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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