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 A005927 Theta series of diamond with respect to deep hole. (Formerly M3262) 6
 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 12, 8, 0, 0, 0, 0, 0, 0, 12, 24, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 24, 30, 0, 0, 0, 0, 0, 0, 12, 24, 0, 0, 0, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 12, 48, 0, 0, 0, 0, 0, 0, 28, 24, 0, 0, 0, 0, 0, 0, 36, 48, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700). REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Michael Somos, Introduction to Ramanujan theta functions N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534. Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of 4 * q^3 * psi^3(q^8) + (phi^3(q^4) - phi^3(-q^4)) / 2 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos, Aug 17 2009 a(8*n + 0) = a(8*n + 1) = a(8*n + 2) = a(8*n + 5) = a(8*n + 6) = a(8*n + 7) = 0. - Michael Somos, Aug 17 2009 4 * A008443(n) = a(8*n + 3). A005887(n) = a(8*n + 4). - Michael Somos, Aug 17 2009 EXAMPLE 4*q^3 + 6*q^4 + 12*q^11 + 8*q^12 + 12*q^19 + 24*q^20 + 16*q^27 + ... - Michael Somos, Aug 17 2009 MATHEMATICA a[n_]:= SeriesCoefficient[4*q^3*QPochhammer[-q^8, q^8]^3* QPochhammer[q^16, q^16]^3 + (EllipticTheta[3, 0, q^4]^3 - EllipticTheta[3, 0, -q^4]^3)/2, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Apr 01 2018 *) PROG (PARI) {a(n) = if( n<0, 0, if( n%8 == 3, n \= 8; polcoeff( 4 * sum(k=0, (sqrtint(8*n+1)-1)\2, x^((k^2+k)/2), x*O(x^n))^3, n), if( n%8 == 4, n /= 4; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1 + x*O(x^n))^3, n), 0 )))} /* Michael Somos, Aug 17 2009 */ CROSSREFS Sequence in context: A299639 A244444 A231407 * A201529 A079207 A259825 Adjacent sequences:  A005924 A005925 A005926 * A005928 A005929 A005930 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 2 14:21 EDT 2020. Contains 334787 sequences. (Running on oeis4.)