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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)