0,1

Repeatedly [1,[0,]^2k,1,[0,]^k], k>=0; characteristic function of generalized pentagonal numbers: a(A001318(n))=1, a(A118300(n))=0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2006

P. A. MacMahon, Combinatory Analysis, Cambridge Univ. Press, London and New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 81, Article 331.

T. D. Noe, Table of n, a(n) for n=0..1001

Index entries for characteristic functions

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

G.f.: Sum x^(n*(3n+1)/2), n=-inf..inf [the exponents are the pentagonal numbers, A000326].

a(n)=b(24n+1) where b(n) is multiplicative and b(2^e)=b(3^e)=0^e, b(p^e)=(1+(-1)^e)/2 if p>3. - Michael Somos Jun 06 2005

Euler transform of period 6 sequence [ 1, 0, -1, 0, 1, -1, ...].

Expansion of phi(-q^3) / chi(-q) in powers of q where phi(), chi() are Ramanujan theta functions. - Michael Somos Sep 14 2007

Expansion of psi(q) - q * psi(q^9) in powers of q^3 where psi() is a Ramanujan theta function. - Michael Somos Sep 14 2007

Expansion of f(x, x^2) in powers of x where f() is Ramanujan's two-variable theta function.

G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 2^(1/2) (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A089810.

Expansion of q^(-1/24) * eta(q^2) * eta(q^3)^2 / (eta(q) * eta(q^6)) in powers of q.

G.f.: Product_{k>0} (1 - x^(3*k)) / (1 - x^k + x^(2*k)). - Michael Somos Jan 26 2008

q + q^25 + q^49 + q^121 + q^169 + q^289 + q^361 + q^529 + q^625 + ...

(PARI) a(n)=if(n<0, 0, abs(polcoeff(eta(x+x*O(x^n)), n)))

(PARI) a(n)=issquare(24*n+1) /* Michael Somos Apr 13 2005 */

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)^2/eta(x+A)/eta(x^6+A), n))}

|A010815(n)| = a(n). A089806(2n) = a(n). A033683(24n+1) = a(n).

Sequence in context: A115513 A133080 A010815 this_sequence A121373 A133985 A143062

Adjacent sequences: A080992 A080993 A080994 this_sequence A080996 A080997 A080998

nonn,easy

Michael Somos, Feb 27, 2003