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Search: id:A005313
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| A005313 |
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Triangular anti-Hadamard matrices of order n.
(Formerly M2573)
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+0
2
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| 1, 3, 6, 13, 29, 70, 175, 449, 1164, 3035, 7931, 20748, 54301, 142143, 372114, 974185, 2550425, 6677074, 17480779, 45765245, 119814936, 313679543, 821223671, 2149991448
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
R. L. Graham and N. J. A. Sloane, Anti-Hadamard matrices, Linear Alg. Applic., 62 (1984), 113-137.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: [x(1-x-3x^2+x^3)]/[(1-3x+x^2)(1+x)(1-x)^2]. - Ralf Stephan, Apr 22 2004
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MAPLE
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A005313:=(1-z-3*z**2+z**3)/(z+1)/(z**2-3*z+1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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a(n) = A064831(n-1) + n.
Sequence in context: A078061 A018909 A093128 this_sequence A108639 A087218 A098075
Adjacent sequences: A005310 A005311 A005312 this_sequence A005314 A005315 A005316
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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