A002096 Mixed partitions of n. (Formerly M0757 N0286)

0, 0, 1, 2, 3, 6, 9, 14, 20, 29, 42, 58, 79, 108, 145, 191, 252, 329, 427, 549, 704, 894, 1136, 1427, 1793, 2237, 2789, 3450, 4268, 5248, 6447, 7880, 9619, 11691, 14199, 17166, 20739, 24966, 30020, 35976, 43076, 51420, 61320, 72927, 86642, 102682

Offset

1,4

Comments

The number of partitions of n with at least one prime part and at least one nonprime part. - Sean A. Irvine, Mar 23 2016

References

L. M. Chawla and S. A. Shad, On a trio-set of partition functions and their tables, J. Natural Sciences and Mathematics, 9 (1969), 87-96.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..46.

Formula

a(n) = Sum_{k=1..n-1} A000607(n - k) * A002095(k). - Sean A. Irvine, Mar 23 2016

Crossrefs

Sequence in context: A226893 A084628 A325269 * A325866 A094055 A094056

Adjacent sequences: A002093 A002094 A002095 * A002097 A002098 A002099

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 23 2016

Status

approved