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%I #7 Mar 07 2022 02:05:59
%S 0,16,40,8,112,160,8,280,352,16,520,616,80,832,952,40,1216,1360,56,
%T 1672,1840,224,2200,2392,32,2800,3016,40,3472,3712,440,4216,4480,176,
%U 5032,5320,208,5920,6232,728,6880,7216,280,7912,8272,320,9016,9400,1088,10192,10600,136,11440,11872,152
%N First bisection of A061039.
%C From Paschen spectrum of hydrogen.
%C All numbers are multiples of 8.
%H G. C. Greubel, <a href="/A144448/b144448.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_81">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F a(n) = A061039(2*n+1).
%F From _G. C. Greubel_, Mar 06 2022: (Start)
%F a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81).
%F a(n) = 8*A178978(n). (End)
%t Table[Numerator[1/3^2 - 1/(2*n+1)^2], {n,100}] (* _G. C. Greubel_, Mar 06 2022 *)
%o (Sage) [numerator(1/9 -1/(2*n+1)^2) for n in (1..100)] # _G. C. Greubel_, Mar 06 2022
%Y Cf. A061039, A178978.
%K nonn
%O 1,2
%A _Paul Curtz_, Oct 06 2008
%E Formula index corrected, extended by _R. J. Mathar_, Dec 02 2008
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