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Search: id:A103924
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| A103924 |
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Number of partitions of n into parts but with two kinds of parts of sizes 1,2,3,4,and 5. |
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+0
8
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| 1, 2, 5, 10, 20, 36, 64, 107, 177, 282, 443, 678, 1026, 1522, 2234, 3231, 4628, 6550, 9193, 12774, 17619, 24098, 32740, 44161, 59213, 78894, 104553, 137787, 180702, 235806, 306354, 396226, 510392, 654787, 836911, 1065734, 1352475, 1710535
(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..5)^2)*product(1/(1-x^j), j=6..infty).
a(n)=sum(A000710(n-5*j), j=0..floor(n/5)), n>=0.
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CROSSREFS
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Sixth column (m=5) 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: A117486 A000710 A117487 this_sequence A103925 A103926 A103927
Adjacent sequences: A103921 A103922 A103923 this_sequence A103925 A103926 A103927
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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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