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Search: id:A136343
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| A136343 |
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a(n) is the number of partitions of n such that each summand is greater than or equal to the sum of the next two summands. |
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+0
1
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| 1, 2, 2, 4, 4, 6, 7, 10, 11, 14, 16, 21, 23, 29, 32, 40, 43, 52, 57, 69, 75, 88, 96, 113, 122, 141, 153, 177, 190, 216, 233, 265, 285, 320
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OFFSET
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1,2
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COMMENT
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This sequence was suggested by Moshe Newman. The idea came to him while reading a paper of Lev Shneerson. The conjectured generating function is also due to Moshe Newman.
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FORMULA
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Conjectured generating function: 1/((1-x)(1-x^2)(1-x^4)(1-x^7)(1-x^12)...) where the exponents in the generating function are the sums of the Fibonacci sequence.
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EXAMPLE
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a(5)=4 because 4 of the 7 partitions of 5 have the required property: {5} {4, 1} {3,2} {3,1,1}. The other 3 partitions of 5: {2,2,1} {2,1,1,1} and {1,1,1,1,1} each have an element which is < the sum of next two.
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CROSSREFS
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Adjacent sequences: A136340 A136341 A136342 this_sequence A136344 A136345 A136346
Sequence in context: A106247 A094909 A029008 this_sequence A001996 A122134 A035940
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KEYWORD
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nonn
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AUTHOR
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David Newman (davidsnewman(AT)gmail.com), May 11 2008
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