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A006501
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Expansion of (1+x^2 ) / (1-x)^2 (1-x^3 )^2.
(Formerly M1091)
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3
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1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 80, 100, 125, 150, 180, 216, 252, 294, 343, 392, 448, 512, 576, 648, 729, 810, 900, 1000, 1100, 1210, 1331, 1452, 1584, 1728, 1872, 2028, 2197, 2366, 2548, 2744, 2940, 3150, 3375, 3600, 3840, 4096, 4352, 4624, 4913, 5202
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n+3) = maximal product of three numbers with sum n: a(n) = max(r*s*t), n = r+s+t. - Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jul 10 2003
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REFERENCES
| G. E. Bergum and V. E. Hoggatt, Jr., A combinatorial problem involving recursive sequences and tridiagonal matrices, Fib. Quart., 16 (1978), 113-118.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| a(n) = [(n+3)/3] * [(n+4)/3] * [(n+5)/3]. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 18 2004
a(n-3) = sum(k=0..n, [k/3][(k+1)/3]). - Mitchell Harris, Dec 02, 2004
Conjecture: a(n) = A144677(n)+A144677(n-2). - R. J. Mathar, Mar 15 2011
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MAPLE
| A006501:=(1+z**2)/(z**2+z+1)**2/(z-1)**4; [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Cf. A002620
Sequence in context: A080476 A053799 A085891 * A074633 A006500 A134181
Adjacent sequences: A006498 A006499 A006500 * A006502 A006503 A006504
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 18 2004
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