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A005313
Maximal sum of inverse squares of the singular values of triangular anti-Hadamard matrices of order n.
(Formerly M2573)
8
1, 3, 6, 13, 29, 70, 175, 449, 1164, 3035, 7931, 20748, 54301, 142143, 372114, 974185, 2550425, 6677074, 17480779, 45765245, 119814936, 313679543, 821223671, 2149991448, 5628750649, 14736260475, 38580030750, 101003831749, 264431464469, 692290561630, 1812440220391, 4745030099513
OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Noga Alon and Van H. Vu, Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs, Journal of Combinatorial Theory, Series A, Volume 79, Issue 1, July 1997, Pages 133-160.
R. L. Graham and N. J. A. Sloane, Anti-Hadamard matrices, Linear Alg. Applic., 62 (1984), 113-137, Table 1.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
a(n) = A064831(n-1) + n.
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]
CROSSREFS
Sequence in context: A078061 A018909 A093128 * A213674 A108639 A327795
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition corrected by Stefano Spezia, Jan 30 2022
STATUS
approved