

A086674


Sum of signed indices from Euler's Pentagonal Theorem (see A000041).


0



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
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OFFSET

1,3


COMMENTS

Is the sequence increasing? (checked to n=5000).


LINKS

Table of n, a(n) for n=1..50.


FORMULA

a(n)=sum{k_i is a generalized pentagonal, (1)^(floor((i+1)/2))*(nk)}


EXAMPLE

a(10) is given via the expansion part(10)=part(9)+part(8)part(5)part(3), so in this sequence a(10)=9+853=9.


PROG

(PARI) { gp=vecsort(vector(20, i, x=10i; x*(3*x1)/2)); for (n=1, 50, s=0; i=1; while (ngp[i+1]>0, s=(1)^(floor((i+1)/2))*(ngp[i+1]); i++); print1(", "s)) }


CROSSREFS

Cf. A001318 (GP's), A000041 (partition function).
Sequence in context: A008508 A163301 A036593 * A137203 A102890 A008520
Adjacent sequences: A086671 A086672 A086673 * A086675 A086676 A086677


KEYWORD

nonn


AUTHOR

Jon Perry, Sep 12 2003


STATUS

approved



