

A244465


Expansion of f(x^3, x^5) in powers of x where f() is Ramanujan's twovariable theta function.


4



1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

0,1


LINKS



FORMULA

Euler transform of period 8 sequence [ 0, 0, 1, 0, 1, 0, 0, 1, ...].
G.f.: f(x^3, x^5) = Sum_{k in Z} (1)^k * x^(4*k^2  k).


EXAMPLE

G.f. = 1  x^3  x^5 + x^14 + x^18  x^33  x^39 + x^60 + x^68  x^95 + ...
G.f. = q  q^49  q^81 + q^225 + q^289  q^529  q^625 + q^961 + q^1089 + ...


MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^3, x^8] QPochhammer[ x^5, x^8] QPochhammer[ x^8], {x, 0, n}];


PROG

(PARI) {a(n) = issquare( 16*n + 1) * (1)^n};


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



