The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A226860 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A226860

Expansion of psi(-x) * phi(-x^6) in powers of x where phi(), psi() are Ramanujan theta functions.
(history; published version)

#16 by Charles R Greathouse IV at Fri Mar 12 22:24:47 EST 2021

LINKS

M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

Discussion

Fri Mar 12

22:24

OEIS Server: https://oeis.org/edit/global/2897

#15 by N. J. A. Sloane at Wed Nov 13 21:58:50 EST 2019

LINKS

M. Somos, <a href="http://somos.crg4.comA010815/multiqa010815.htmltxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

21:58

OEIS Server: https://oeis.org/edit/global/2832

#14 by Michael Somos at Fri Aug 10 01:07:56 EDT 2018

STATUS

editing

approved

#13 by Michael Somos at Fri Aug 10 01:07:27 EDT 2018

FORMULA

Euler transform of period 12 sequence [ -1, 0, -1, -1, -1, -2, -1, -1, -1, 0, -1, -2, ...].

PROG

(PARI) {a(n) = my(A, p, e, i); if( n<0, 0, n = 8*n + 1; A = factor(n); prod( k=1, matsize(A)[1], if( [p = A[k, 1], , e ] = A[k, 2 ]; if( p==2, 0, if( p==3, I^e, if( p%24 == 1 || p%24==19, for(j=1, sqrtint(p\18), if( issquare( p - 18*j^2, &i), break)); (e+1) * (if(p%24==1, 1, -I) * kronecker( 12, i))^e, if( e%2, 0, if(p%24>12, 1, -1)^(e/2)))) )) ))}; /* Michael Somos, Sep 08 2014 */

STATUS

proposed

editing

Discussion

Fri Aug 10

01:07

Michael Somos: Space edit. Updated my PARI code with tweaks.

#12 by G. C. Greubel at Thu Aug 09 23:49:38 EDT 2018

STATUS

editing

proposed

#11 by G. C. Greubel at Thu Aug 09 23:49:32 EDT 2018

LINKS

G. C. Greubel, <a href="/A226860/b226860.txt">Table of n, a(n) for n = 0..2500</a>

STATUS

approved

editing

#10 by Michael Somos at Sat Apr 25 19:03:42 EDT 2015

STATUS

editing

approved

#9 by Michael Somos at Sat Apr 25 19:03:30 EDT 2015

LINKS

M. Somos, <a href="http://cis.csuohio.edu/~somos.crg4.com/multiq.pdfhtml">Introduction to Ramanujan theta functions</a>

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^6] EllipticTheta[ 2, Pi/4, q^(1/2)] / (Sqrt[2] q^(1/8)) , , {q, 0, n}];

PROG

(PARI) {a(n) = localmy(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^2 / (eta(x^2 + A) * eta(x^12 + A)), n))};

(PARI) {a(n) = localmy(A, p, e, i); if( n<0, 0, n = 8*n + 1; A = factor(n); prod( k=1, matsize(A)[1], if( p = A[k, 1], e = A[k, 2]; if( p==2, 0, if( p==3, I^e, if( p%24 == 1 || p%24==19, for(j=1, sqrtint(p\18), if( issquare( p - 18*j^2, &i), break)); (e+1) * (if(p%24==1, 1, -I) * kronecker( 12, i))^e, if( e%2, 0, if(p%24>12, 1, -1)^(e/2)))) ))))}; /* Michael Somos, Sep 08 2014 */

STATUS

approved

editing

Discussion

Sat Apr 25

19:03

Michael Somos: Light and space edits. Revised URL.

#8 by Michael Somos at Mon Sep 08 22:06:03 EDT 2014

STATUS

editing

approved

#7 by Michael Somos at Mon Sep 08 22:05:54 EDT 2014

FORMULA

a(3*n) = A226289(n). a(3*n + 1) = - A246962(n). a(3*n + 2) = 0.

CROSSREFS

Cf. A226350, A226289, A246962.

STATUS

approved

editing

Discussion

Mon Sep 08

22:06

Michael Somos: Added more info.