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Search: id:A089299
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| A089299 |
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Number of square partitions of n. |
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+0
3
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| 1, 1, 1, 1, 2, 2, 4, 5, 8, 11, 16, 21, 31, 41, 57, 78, 108, 146, 202, 274, 375, 509, 690, 929, 1255, 1679, 2246, 2991, 3979, 5266, 6971, 9187, 12104, 15898, 20870, 27322, 35762, 46690, 60927, 79348, 103270, 134138, 174108, 225576, 291990, 377320, 487083
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Number of ways of writing n as a sum p(1,1) + p(1,2) + ... + p(1,k) + p(2,1) + ... + p(2,k) + ... + p(k,1) + ... + p(k,k) for some k so that in the square array {p(i,j)} the numbers are nonincreasing along rows and columns. All the p(i,j) are >= 1.
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FORMULA
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Is there a recurrence or g.f.?
G.f. sum_{k=0}^{infinity} x^{k^2)/product_{j=1}^{2k-1} (1-x^j)^min(j,2k-j). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 14 2006
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EXAMPLE
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a(7) = 5:
7 41 32 31 22
. 11 11 21 21
a(10) = 16 from {{10}}, {{3, 2}, {3, 2}}, {{3, 3}, {2, 2}}, {{3, 3}, {3, 1}}, {{4, 1}, {4, 1}}, {{4, 2}, {2, 2}}, {{4, 2}, {3, 1}}, {{4, 3}, {2, 1}}, {{4, 4}, {1, 1}}, {{5, 1}, {3, 1}}, {{5, 2}, {2, 1}}, {{5, 3}, {1, 1}}, {{6, 1}, {2, 1}}, {{6, 2}, {1, 1}}, {{7, 1}, {1, 1}}, {{2, 1, 1}, {1, 1, 1}, {1, 1, 1}}}
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CROSSREFS
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Cf. A008763, A001970, A089292.
Adjacent sequences: A089296 A089297 A089298 this_sequence A089300 A089301 A089302
Sequence in context: A027193 A126796 A109434 this_sequence A017910 A013979 A107458
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KEYWORD
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nonn
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AUTHOR
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njas, Dec 25 2003
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EXTENSIONS
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Corrected and extended by Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 30 2003
a(21)-a(25) from John W. Layman (layman(AT)math.vt.edu), Jan 02 2004
More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 14 2006
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