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Search: id:A131996
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| A131996 |
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Number of partitions of n into distinct powers of 2 or of 3. |
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+0
4
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| 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(A081601(n)) = n+1 and a(m) < n+1 for m < A081601(n).
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..1000
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FORMULA
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G.f.=Product((1+x^(2^k))(1+x^(3^k)),k=0..infinity)/(1+x) (offset 0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 26 2007
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EXAMPLE
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a(10)=#{9+1,8+2,4+3+2+1}=3;
a(20)=#{16+4,16+3+1,9+8+3,9+8+2+1}=4;
a(30)=#{27+3,27+2+1,16+9+4+1,16+9+3+2,16+8+4+2,16+8+3+2+1}=6.
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MAPLE
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g:=(product((1+x^(2^k))*(1+x^(3^k)), k=0..10))/(1+x): gser:=series(g, x=0, 111): seq(coeff(gser, x, n), n=1..108); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 26 2007
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CROSSREFS
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Cf. A062051, A106244, A000009, A131995.
Sequence in context: A051742 A134119 A064661 this_sequence A090618 A072748 A030603
Adjacent sequences: A131993 A131994 A131995 this_sequence A131997 A131998 A131999
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 06 2007
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