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A103926 Number of partitions of n into parts but with two kinds of parts of sizes 1 to 7. +0
1
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)
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. 90.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.

FORMULA

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.

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

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

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Last modified November 29 12:46 EST 2009. Contains 167659 sequences.


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