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Search: id:A086674
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| A086674 |
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Sum of signed indices from Euler's Pentagonal Theorem (see A000041). |
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+0
1
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| 0, 1, 3, 5, 7, 8, 9, 9, 9, 9, 9, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Is the sequence increasing? (checked to n=5000).
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FORMULA
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a(n)=sum{k_i is a generalized pentagonal, (-1)^(floor((i+1)/2))*(n-k)}
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EXAMPLE
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a(10) is given via the expansion part(10)=part(9)+part(8)-part(5)-part(3), so in this sequence a(10)=9+8-5-3=9.
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PROGRAM
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(PARI) { gp=vecsort(vector(20, i, x=10-i; x*(3*x-1)/2)); for (n=1, 50, s=0; i=1; while (n-gp[i+1]>0, s-=(-1)^(floor((i+1)/2))*(n-gp[i+1]); i++); print1(", "s)) }
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CROSSREFS
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Cf. A001318 (GP's), A000041 (partition function).
Sequence in context: A101496 A008508 A036593 this_sequence A137203 A102890 A008520
Adjacent sequences: A086671 A086672 A086673 this_sequence A086675 A086676 A086677
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Sep 12 2003
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