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Search: id:A103928
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| A103928 |
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Number of partitions of n into parts but with two kinds of parts of sizes 1 to 9. |
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+0
1
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| 1, 2, 5, 10, 20, 36, 65, 110, 185, 300, 480, 749, 1157, 1752, 2627, 3882, 5683, 8221, 11796, 16756, 23627, 33036, 45881, 63257, 86689, 118036, 159837, 215211, 288314, 384275, 509829, 673270, 885361, 1159357, 1512235, 1964897, 2543864, 3281686
(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..9)^2)*product(1/(1-x^j), j=10..infty).
a(n)=sum(A103924(n-9*j), j=0..floor(n/9)), n>=0.
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CROSSREFS
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Tenth column (m=9) 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).
Adjacent sequences: A103925 A103926 A103927 this_sequence A103929 A103930 A103931
Sequence in context: A103925 A103926 A103927 this_sequence A103929 A121597 A000712
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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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