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Search: id:A103929
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| A103929 |
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Number of partitions of n into parts but with two kinds of parts of sizes 1 to 10. |
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+0
3
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| 1, 2, 5, 10, 20, 36, 65, 110, 185, 300, 481, 751, 1162, 1762, 2647, 3918, 5748, 8331, 11981, 17056, 24108, 33787, 47043, 65019, 89336, 121954, 165585, 223542, 300295, 401331, 533937, 707057, 932404, 1224376, 1601571, 2086851, 2709449, 3505228
(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. 91.
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..10)^2)*product(1/(1-x^j), j=11..infty).
a(n)=sum(A103924(n-1o*j), j=0..floor(n/10)), n>=0.
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CROSSREFS
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Eleventh column (m=10) 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: A103926 A103927 A103928 this_sequence A121597 A000712 A032442
Adjacent sequences: A103926 A103927 A103928 this_sequence A103930 A103931 A103932
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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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