id:A028586 - OEIS Search Results

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Theta series of lattice with Gram matrix [2 1; 1 3].

+0
4

1, 0, 2, 4, 0, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 8, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 8, 4, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 8, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4 (list; graph; listen)

	OFFSET	`0,3`
	LINKS	`John Cannon, Table of n, a(n) for n = 0..10000` `A. Berkovich and H. Yesilyurt, Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms`
	FORMULA	`Expansion of (theta_3(z)theta_3(5z)+theta_2(z)theta_2(5z)).` `Expansion of phi(q^2)phi(q^10) +4q^3psi(q^4)psi(q^20) in powers of q where phi(q),psi(q) are Ramanujan theta functions. - Michael Somos Aug 13 2006` `If p is prime then a(p) is nonzero iff p is in A106865.` `0=a(n)a(2n) and 2*A035170(n)=a(n)+a(2n) if n>0. - Michael Somos Oct 21 2006`
	EXAMPLE	`1 + 2q^2 + 4q^3 + 4q^7 + 2q^8 + 2q^10 + 4q^12 + 4q^15 + 6q^18 + 4q^23 + 8q^27 + 4q^28 + 2q^32 + 4q^35 + 2q^40 + 8q^42 + 4q^43 + 4*q^47 + ...`
	PROGRAM	`(PARI) {a(n)=if(n<1, n==0, qfrep([2, 1; 1, 3], n)[n]2)} / Michael Somos Aug 13 2006 */`
	CROSSREFS	`Adjacent sequences: A028583 A028584 A028585 this_sequence A028587 A028588 A028589` `Sequence in context: A138758 A107501 A126732 this_sequence A072069 A004025 A102561`
	KEYWORD	`nonn`
	AUTHOR	`njas`

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Last modified May 16 01:24 EDT 2008. Contains 139630 sequences.

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