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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 (list; graph; refs; listen; history; text; internal format)
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))*(n-k)}

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+8-5-3=9.

PROG

(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)) }

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

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Last modified June 15 19:31 EDT 2021. Contains 345049 sequences. (Running on oeis4.)