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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A178798 A318277 A233321

Adjacent sequences:  A174653 A174654 A174655 * A174657 A174658 A174659

KEYWORD

nonn

AUTHOR

Wouter Meeussen, Mar 25 2010

STATUS

approved

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Last modified June 20 08:57 EDT 2021. Contains 345162 sequences. (Running on oeis4.)