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Maximal sum of inverse squares of the singular values of triangular anti-Hadamard matrices of order n.
(Formerly M2573)
8

%I M2573 #30 Apr 13 2022 13:25:17

%S 1,3,6,13,29,70,175,449,1164,3035,7931,20748,54301,142143,372114,

%T 974185,2550425,6677074,17480779,45765245,119814936,313679543,

%U 821223671,2149991448,5628750649,14736260475,38580030750,101003831749,264431464469,692290561630,1812440220391,4745030099513

%N Maximal sum of inverse squares of the singular values of triangular anti-Hadamard matrices of order n.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Noga Alon and Van H. Vu, <a href="https://doi.org/10.1006/jcta.1997.2780">Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs</a>, Journal of Combinatorial Theory, Series A, Volume 79, Issue 1, July 1997, Pages 133-160.

%H R. L. Graham and N. J. A. Sloane, <a href="http://dx.doi.org/10.1016/0024-3795(84)90090-9">Anti-Hadamard matrices</a>, Linear Alg. Applic., 62 (1984), 113-137, Table 1.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-3,4,-1).

%F a(n) = A064831(n-1) + n.

%F G.f.: [x(1-x-3x^2+x^3)]/[(1-3x+x^2)(1+x)(1-x)^2]. - Conjectured by _Simon Plouffe_ in his 1992 dissertation. [This is in fact the correct g.f. - _N. J. A. Sloane_, Jan 28 2022]

%Y Cf. A005312, A064831.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E Definition corrected by _Stefano Spezia_, Jan 30 2022