A086674 Sum of signed indices from Euler's Pentagonal Theorem (see A000041).

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

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