id:A108563 - OEIS Search Results

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Number of representations of n as sum of twice a square plus thrice a square.

+0
1

0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, 0, 0, 2, 0, 4, 4, 0, 2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 0, 6, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 8, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4 (list; graph; listen)

	OFFSET	`0,3`
	LINKS	`A. Berkovich and H. Yesilyurt, Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms`
	FORMULA	`G.f.: 1 + Sum_{k>0} x^k(1+x^(4k))(1+x^(6k))/(1+x^(12k)) - Sum_{k>0} kronecker(k,3)*x^k(1-x^(2k))/(1+x^(4k))` `Expansion of phi(q^2)phi(q^3) where phi() is a Ramanujan theta function.`
	PROGRAM	`(PARI) for(n=0, 120, print1(if(n<1, 0, qfrep([2, 0; 0, 3], n)[n]*2), ", "))`
	CROSSREFS	`Cf. a(n) = A000377(n) - A115660(n).` `Sequence in context: A011137 A143396 A090657 this_sequence A138476 A131381 A112080` `Adjacent sequences: A108560 A108561 A108562 this_sequence A108564 A108565 A108566`
	KEYWORD	`nonn`
	AUTHOR	`Ralf Stephan, May 13 2007`
	EXTENSIONS	`Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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