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Search: id:A000710
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| A000710 |
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Number of partitions of n, with two kinds of 1,2,3 and 4.
(Formerly M1375 N0535)
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+0
9
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| 1, 2, 5, 10, 20, 35, 62, 102, 167, 262, 407, 614, 919, 1345, 1952, 2788, 3950, 5524, 7671, 10540, 14388, 19470, 26190, 34968, 46439, 61275, 80455, 105047, 136541, 176593, 227460, 291673, 372605, 474085, 601105, 759380, 956249, 1200143
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also number of partitions of 2*n+4 with exactly 4 odd parts. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2005
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 90.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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Euler transform of 2 2 2 2 1 1 1...
G.f.=1/[(1-x)(1-x^2)(1-x^3)(1-x^4)*product((1-x^k), k=1..infinity)].
a(n)=sum(A000098(n-4*j), j=0..floor(n/4)), n>=0.
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EXAMPLE
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a(2)=5 because we have 2, 2', 1+1, 1+1', 1+1'.
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MAPLE
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with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr (n-> `if`(n<5, 2, 1)): seq (a(n), n=0..37); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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CROSSREFS
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Cf. A000712.
Cf. A000070, A008951, A000097, A000098.
Fifth column of Riordan triangle A008951 and of triangle A103923.
Sequence in context: A039690 A126105 A117486 this_sequence A117487 A103924 A160647
Adjacent sequences: A000707 A000708 A000709 this_sequence A000711 A000712 A000713
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 22 2005
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