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Search: id:A103928
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A103928 Number of partitions of n into parts but with two kinds of parts of sizes 1 to 9. +0
1
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)
OFFSET

0,2

COMMENT

See A103923 for other combinatorial interpretations of a(n).

REFERENCES

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.

FORMULA

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.

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Mar 24 2005

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Last modified May 16 01:24 EDT 2008. Contains 139630 sequences.


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