A005313 - OEIS

A005313

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

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

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OFFSET

1,2

REFERENCES

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

LINKS

Table of n, a(n) for n=1..32.

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

Index entries for linear recurrences with constant coefficients, signature (4,-3,-3,4,-1).

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

Cf. A005312, A064831.

Sequence in context: A078061 A018909 A093128 * A213674 A108639 A327795

Adjacent sequences: A005310 A005311 A005312 * A005314 A005315 A005316

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Definition corrected by Stefano Spezia, Jan 30 2022

STATUS

approved