A285635 G.f.: (1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - ...))))) / (1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + ...))))), a continued fraction.

1, -2, 2, -2, 0, 0, -2, 2, -4, 0, -2, -6, 0, -10, -6, -12, -20, -20, -40, -46, -68, -104, -132, -204, -280, -394, -578, -790, -1154, -1616, -2294, -3286, -4614, -6610, -9340, -13278, -18878, -26748, -38060, -53978, -76684, -108912, -154600, -219622, -311812, -442818, -628866, -892962, -1268168

Offset

0,2

Links

Table of n, a(n) for n=0..48.

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Formula

G.f.: A(x) = R(x)*Q(x)/P(x), where R(x) = Product_{k>=1} (1 - x^(5*k-1))*(1 - x^(5*k-4)) / ((1 - x^(5*k-2))*(1 - x^(5*k-3)), Q(x) = Sum_{k>=0} (-1)^k*x^(k^2) / Product_{m=1..k} (1 - x^m) and P(x) = Sum_{k>=0} (-1)^k*x^(k*(k+1)) / Product_{m=1..k} (1 - x^m).

Example

G.f.: A(x) = 1 - 2*x + 2*x^2 - 2*x^3 - 2*x^6 + 2*x^7 - 4*x^8 - 2*x^10 - 6*x^11 - ...

Mathematica

nmax = 48; CoefficientList[Series[(1/(1 + ContinuedFractionK[x^k, 1, {k, 1, nmax}]))/(1/(1 + ContinuedFractionK[-x^k, 1, {k, 1, nmax}])), {x, 0, nmax}], x]
nmax = 48; CoefficientList[Series[Product[(1 - x^(5 k - 1)) (1 - x^(5 k - 4))/((1 - x^(5 k - 2)) (1 - x^(5 k - 3))), {k, 1, nmax}] Sum[(-1)^k x^(k^2)/Product[(1 -
x^m), {m, 1, k}], {k, 0, nmax}] / Sum[(-1)^k x^(k (k + 1))/Product[(1 - x^m), {m, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A003823, A005169, A007325, A055101, A285636, A285637, A285638.

Sequence in context: A178045 A321300 A037864 * A181674 A181676 A262048

Adjacent sequences: A285632 A285633 A285634 * A285636 A285637 A285638

Keyword

sign

Author

Ilya Gutkovskiy, Apr 23 2017

Status

approved