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A144416
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a(n) = total number of partitions of [1, 2, ..., k] into exactly n blocks, each of size 1, 2 or 3, for 0 <= k <= 3n.
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10
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1, 3, 31, 842, 45296, 4061871, 546809243, 103123135501, 25942945219747, 8394104851717686, 3395846808758759686, 1679398297627675722593, 996789456118195908366641, 699283226713639676370419067, 572385833490097906671186099971, 540635257271794961275858251107746, 583630397618757664934692641037584628
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| David Applegate and N. J. A. Sloane, Table of n, a(n) for n = 0..100
David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009)
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FORMULA
| a(n) = Sum_{ b,c >= 0, b+c <= n } (n+b+2c)!/ ((n-b-c)! b! c! 2^b 6^c).
The sum is dominated by the b=0, c=n term, so a(n) ~ constant*(3*n)!/(n!*6^n).
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EXAMPLE
| a(0) = 1;
a(1) = 3: {1} {12} {123}
a(2) = 31: {1,2} {1,23} {2,13} {3,12} {1,234} {2,134} {3,124} {4,123}
{12,34} {13,24} {14,23} {12,345} {13,245} {14,235} {15,234} {23,145} {24,135}
{25,134} {34,125} {35,124} {45,123} {123,456} {124,356} {125,346} {126,345}
{134,256} {135,246} {136,245} {145,236} {146,235} {156,234}.
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CROSSREFS
| Row sums of A144385. Slice sums of A144626.
Sequence in context: A092552 A196457 A136370 * A022514 A094579 A029729
Adjacent sequences: A144413 A144414 A144415 * A144417 A144418 A144419
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KEYWORD
| nonn
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AUTHOR
| David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Dec 07 2008, Dec 17 2008
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