The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A005928 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A005928

G.f.: s(1)^3/s(3), where s(k) = eta(q^k) and eta(q) is Dedekind's function, cf. A010815.
(history; published version)

#73 by Charles R Greathouse IV at Thu Sep 08 08:44:34 EDT 2022

PROG

(MAGMAMagma) A := Basis( ModularForms( Gamma1(9), 1), 100); A[1] - 3*A[2] + 6*A[4]; \\ Michael Somos, Jan 31 2015

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#72 by R. J. Mathar at Mon Feb 22 09:09:51 EST 2021

STATUS

proposed

approved

#71 by Michel Marcus at Mon Feb 22 07:19:51 EST 2021

STATUS

editing

proposed

#70 by Michel Marcus at Mon Feb 22 07:19:46 EST 2021

FORMULA

a(n) is the coefficient of q^n in b(q)=eta(q)^3/eta(q^3) = (3/2)*a(q^3)-a(q)/2 where a(q)=theta(Hexagonal) . - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 07 2002

STATUS

proposed

editing

#69 by R. J. Mathar at Mon Feb 22 06:57:47 EST 2021

STATUS

editing

proposed

#68 by R. J. Mathar at Mon Feb 22 06:57:42 EST 2021

FORMULA

a(n) = -3 * b(n) except for a(0) = 1, where b() =A123477() is multiplicative with b(p^e) = -2 if p = 3 and e>0, b(p^e) = e+1 if p == 1 (mod 6), b(p^e) = (1 + (-1)^e)/2 if p == 2, 5 (mod 6).

STATUS

approved

editing

#67 by N. J. A. Sloane at Tue May 08 07:34:07 EDT 2018

STATUS

proposed

approved

#66 by M. F. Hasler at Mon May 07 19:03:44 EDT 2018

STATUS

editing

proposed

#65 by M. F. Hasler at Mon May 07 19:03:10 EDT 2018

EXTENSIONS

Name edited Edited by M. F. Hasler, May 07 2018

#64 by M. F. Hasler at Mon May 07 19:00:11 EDT 2018

FORMULA

From Michael Somos, May 20 2005: (Start)

Euler transform of period 3 sequence [ -3, -3, -2, ...]. - _Michael Somos_, May 20 2005

a(n) = -3 * b(n) except for a(0) = 1, where b() is multiplicative with a(0) = 1 and b(p^e) = -2 if p = 3 and e>0, b(p^e) = e+1 if p == 1 (mod 6), b(p^e) = (1 + (-1)^e)/2 if p == 2, 5 (mod 6). - _Michael Somos_, May 20 2005

G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = v^3 - 2*u*w^2 + u^2*w. - _Michael Somos_, May 20 2005

G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6) = u1^2*u6 - 2*u1*u2*u6 + 4*u2^2*u6 - 3*u2*u3^2. - _Michael Somos_, May 20 2005

G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6) = u1*u2*u3 + u1^2*u3 - 3*u1*u6^2 + u2^2*u3. - _Michael Somos_, May 20 2005(End)