A002096 Mixed partitions of n.

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

Author

N. J. A. Sloane

Keywords

• nonn

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).

Formula

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

Extensions

More terms from Sean A. Irvine, Mar 23 2016