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A080964 Euler transform of period-16 sequence [2,-3,2,1,2,-3,2,-6,2,-3,2,1,2,-3,2,-3,...]. 3
1, 2, 0, 0, 4, 4, 0, 0, 2, -2, 0, 0, -8, -4, 0, 0, -4, 0, 0, 0, 8, -8, 0, 0, -8, -2, 0, 0, -16, 4, 0, 0, 6, -8, 0, 0, 12, 4, 0, 0, 8, 8, 0, 0, -8, 4, 0, 0, -8, 2, 0, 0, 24, -4, 0, 0, 0, 8, 0, 0, -16, 4, 0, 0, 12, 8, 0, 0, 16, 0, 0, 0, 10, -8, 0, 0, -24, 0, 0, 0, -8, -6, 0, 0, 16, 8, 0, 0, -24, -8, 0, 0, -16, -8, 0, 0, 8, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (1501 terms from G. C. Greubel)

FORMULA

a(4*n+2) = a(4*n+3) = 0.

a(n) = 2*A072071(n) - A072070(n).

a(4*n) = A080965(n).

a(4*n+1) = 2*A080966(n).

Expansion of eta(q^2)^5*eta(q^8)^7/(eta(q)^2*eta(q^4)^4*eta(q^16)^3) in powers of q. - G. C. Greubel, Jul 02 2018

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[eta[q^2]^5 *eta[q^8]^7/(eta[q]^2*eta[q^4]^4*eta[q^16]^3), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jul 02 2018 *)

PROG

(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X)^-2*eta(X^2)^5*eta(X^4)^-4*eta(X^8)^7*eta(X^16)^-3, n))

CROSSREFS

Sequence in context: A072740 A226288 A185146 * A134014 A004531 A072071

Adjacent sequences:  A080961 A080962 A080963 * A080965 A080966 A080967

KEYWORD

sign

AUTHOR

Michael Somos, Feb 28 2003

STATUS

approved

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Last modified August 20 10:00 EDT 2019. Contains 326143 sequences. (Running on oeis4.)