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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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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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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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