1,11

Also number of solutions to the equation x+7y=n in triangular numbers give the same sequence offset by 1. E.g. for n=10, 3+7*1=10+7*0=10 so there are two solutions.

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 303.

Expansion of (eta(q^2)eta(q^14))^2/(eta(q)eta(q^7)) in powers of q.

Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -28.

G.f.: Sum_{n>0} (x^n-x^(3n)-x^(5n)+x^(9n)+x^(11n)-x^(13n))/(1-x^(14n)).

Multiplicative with a(2^e) = a(7^e) = 1, a(p^e) = e+1 if p == 1, 2, 4 (mod 7), a(p^e) = (1+(-1)^e)/2 if p == 3, 5, 6 (mod 7). - Michael Somos Sep 10 2005

Euler transform of period 14 sequence [1, -1, 1, -1, 1, -1, 2, -1, 1, -1, 1, -1, 1, -2, ...].

Expansion of q*psi(q)psi(q^7) where psi(q) is a Ramanujan theta function.

a(2n)=a(7n)=a(n). a(7n+3)=a(7n+5)=a(7n+6)=0.

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1^3*u6-u2^3*u3-3*u1*u6^3+3*u2*u3^3+3*u2*u6*(u1*(u2-u1)+3*u3*(u6-u3)) . - Michael Somos Sep 10 2005

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=u*w*(u-2*v)-v*(v-2*w)^2. - Michael Somos Sep 10 2005

G.f.: Sum_{k>0} x^k(1-x^(2k))(1-x^(4k))(1-x^(6k))/(1-x^(14k)) = x Product_{k>0} (1-x^(2k))(1-x^(14k))/((1-x^(2k-1))(1-x^(14k-7))).

For n=11, 5^2+7*3^2=9^2+7*1^2=8*11 so a(11)=2.

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-28, d)))

(PARI) a(n)=if(n<0, 0, sum(i=1, sqrtint(8*n\7), (i%2)*issquare(8*n-7*i^2)))

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-X)/(1-kronecker(-28, p)*X))[n])

Sequence in context: A119395 A087476 A033766 this_sequence A121454 A025462 A024879

Adjacent sequences: A035159 A035160 A035161 this_sequence A035163 A035164 A035165

nonn,mult

njas

Entry revised by njas, Jul 31 2006