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Search: id:A103925
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| A103925 |
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Number of partitions of n into parts but with two kinds of parts of sizes 1,2,3,4,5 and 6. |
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+0
1
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| 1, 2, 5, 10, 20, 36, 65, 109, 182, 292, 463, 714, 1091, 1631, 2416, 3523, 5091, 7264, 10284, 14405, 20035, 27621, 37831, 51425, 69497, 93299, 124588, 165408, 218533, 287231, 375851, 489525, 634980, 820195, 1055444, 1352965, 1728326, 2200060
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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See A103923 for other combinatorial interpretations of a(n).
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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 (reprinted 1962), p. 90.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.
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FORMULA
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G.f.: (product(1/(1-x^k), k=1..6)^2)*product(1/(1-x^j), j=7..infty).
a(n)=sum(A103924(n-6*j), j=0..floor(n/6)), n>=0.
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CROSSREFS
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Seventh column (m=6) of Fine-Riordan triangle A008951, of triangle A103923, i.e. the p_2(n, m) array of the Gupta et al. reference.
Cf. A000712(all parts of two kinds).
Sequence in context: A117487 A103924 A160647 this_sequence A103926 A103927 A103928
Adjacent sequences: A103922 A103923 A103924 this_sequence A103926 A103927 A103928
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Mar 24 2005
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