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Search: id:A103926
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| A103926 |
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Number of partitions of n into parts but with two kinds of parts of sizes 1 to 7. |
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+0
1
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| 1, 2, 5, 10, 20, 36, 65, 110, 184, 297, 473, 734, 1127, 1696, 2526, 3707, 5388, 7737, 11018, 15532, 21731, 30147, 41538, 56813, 77234, 104317, 140120, 187139, 248680, 328769, 432664, 566759, 739297, 960315, 1242583, 1601645, 2057095, 2632724
(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..7)^2)*product(1/(1-x^j), j=8..infty).
a(n)=sum(A103924(n-7*j), j=0..floor(n/7)), n>=0.
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CROSSREFS
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Eighth column (m=7) of Fine-Riordan triangle A008951 and 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: A103924 A160647 A103925 this_sequence A103927 A103928 A103929
Adjacent sequences: A103923 A103924 A103925 this_sequence A103927 A103928 A103929
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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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