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A156039
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Number of partitions of n into 4 ordered summands, where the first is at least as great as each of the others.
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4
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1, 1, 4, 7, 11, 17, 26, 35, 48, 63, 81, 102, 127, 154, 187, 223, 263, 308, 359, 413, 474, 540, 612, 690, 775, 865, 964, 1069, 1181, 1301, 1430, 1565, 1710, 1863, 2025, 2196, 2377, 2566, 2767, 2977, 3197, 3428, 3671, 3923, 4188, 4464, 4752, 5052, 5365, 5689
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For n=1,2 these are just the tetrahedral numbers. a(n) is always at least 1/4 of the corresponding tetrahedral number, since each partition of this type gives up to four ordered partitions with the same cyclical order.
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FORMULA
| G.f.: (x^4-x^3+3*x^2-x+1) / (x^9-2*x^8+x^7-x^6+x^5+x^4-x^3+x^2-2*x+1). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 14 2009]
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EXAMPLE
| For n = 3 the a(3) = 7 partitions are: (3 0 0 0) (2 1 0 0) (2 0 1 0) (2 0 0 1) (1 1 1 0) (1 1 0 1) (1 0 1 1)
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MAPLE
| a:= proc(n) local m, r; m:= iquo (n, 12, 'r'); r:= r+1; (9 +(27 +72*m +18*r)*m +((9 +3*r) *r-12) /2)*m +[1, 1, 4, 7, 11, 17, 26, 35, 48, 63, 81, 102][r] end: seq (a(n), n=0..60); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 14 2009]
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CROSSREFS
| For partitions into 3 summands see A156040; also see A156041 and A156042.
Sequence in context: A171452 A049648 A133257 * A023666 A023502 A024882
Adjacent sequences: A156036 A156037 A156038 * A156040 A156041 A156042
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KEYWORD
| nonn
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AUTHOR
| Jack Grahl (jgrahl(AT)math.ucl.ac.uk), Feb 02 2009, Feb 11 2009
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 14 2009
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