A174656 a(n) counts strict partitions of n into powers of 3^t, 5^f and 7^s with positive exponents t, f and s.

0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 2, 1, 2, 2, 1, 3, 0, 3, 1, 2, 2, 1, 2, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 0, 3, 1, 2, 3, 1, 4, 0, 4, 2, 3, 3, 1, 4, 0, 3, 1, 2, 2, 0, 2, 1, 1, 0, 1, 1

Offset

1,12

Comments

The sequence is symmetric over several ranges: a(n) = a(2271-n) for n > 84; a(n) = a(16545-n) for n > 920; a(n) = a(68660-n) for n > 9611. (Quote from Don Reble: "It's symmetric because 2271 = 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 5^1 + 5^2 + 5^3 + 5^4 + 7^1 + 7^2 + 7^3. That is, all powers less than 2187 (=3^7) contribute. So for any partition of n, with (2271-2187) < n < 2187, there's a complementary partition for 2271-n.")

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..10000

Example

a(100)=2 since 100 = 3 + 3^2 + 3^3 + 5 + 7 + 7^2 and 100 = 3 + 3^2 + 3^4 + 7.

Mathematica

n=512; it=Rest@ CoefficientList[Series[ Product[1+x^(3^k), {k, Ceiling[Log[3, n]]}]* Product[1+x^(5^k), {k, Ceiling[Log[5, n]]}]* Product[1+x^(7^k), {k, Ceiling[Log[7, n]]}], {x, 0, n}], x]

Crossrefs

Sequence in context: A231122 A178686 A142724 * A364047 A373335 A178798

Adjacent sequences: A174653 A174654 A174655 * A174657 A174658 A174659

Keyword

nonn

Author

Wouter Meeussen, Mar 25 2010

Status

approved