|
%I #18 Mar 12 2021 22:24:48
%S 0,0,0,0,1,0,-1,0,-1,1,0,0,0,0,0,-1,-1,0,1,-2,1,1,1,0,0,0,2,0,1,1,0,1,
%T -1,-1,-2,0,1,0,0,-1,-1,-1,-1,1,-1,-1,-3,1,0,0,0,1,0,0,1,3,-2,0,1,-1,
%U 1,1,0,0,1,-1,1,0,0,1,1,-1,0,0,1,3,5,-1,-2,0,0
%N a(n) = A286131(n) + A286132(n).
%C Michael Somos found a four term identity: eta(q) * eta(q^30) * eta(q^35) * eta(q^42) + eta(q^3) * eta(q^10) * eta(q^14) * eta(q^105) = eta(q^2) * eta(q^15) * eta(q^21) * eta(q^70) + eta(q^5) * eta(q^6) * eta(q^7) * eta(q^210).
%H Seiichi Manyama, <a href="/A286135/b286135.txt">Table of n, a(n) for n = 0..10000</a>
%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/retaprod.html">A Remarkable eta-product Identity</a>
%F a(n) = A286133(n) + A286134(n).
%t eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/2) *eta[q^3]*eta[q^10]*eta[q^14]*eta[q^105] + q^(-1/2)*eta[q]*eta[q^30] *eta[q^35]*eta[q^42], {q, 0, 50}], q] (* _G. C. Greubel_, Jul 29 2018 *)
%o (PARI) q='q+O('q^50); A = q*eta(q^3)*eta(q^10)*eta(q^14)*eta(q^105); B = eta(q)*eta(q^30)*eta(q^35)*eta(q^42); concat(vector(4), Vec(A + B)) \\ _G. C. Greubel_, Jul 29 2018
%Y Cf. A286131, A286132, A286133, A286134.
%K sign
%O 0,20
%A _Seiichi Manyama_, May 03 2017
|
