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Undid revision 1239034193 by SB-Euler (talk) no, this is not right: the sum is over *both positive and negative k*, the negative values of k account for the terms you (mistakenly) think are missing |
→Recurrence relations: include alternate form -- maybe this will prevent people from changing this to something wrong? |
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coming from the nonzero values of <math>k</math> in the range
<math display="block"> - \frac{\sqrt{24n+1}-1}{6} \leq k \leq \frac{\sqrt{24n+1}+1}{6}.</math>
The recurrence relation can also be written in the equivalent form
<math display="block">
p(n) = \sum_{k = 1}^\infty (-1)^{k+1} \big(p(n-k(3k-1)/2) + p(n-k(3k+1)/2)\big) .
</math>
Another recurrence relation for <math>p(n)</math> can be given in terms of the [[divisor function|sum of divisors function]] {{math|''σ''}}:{{r|wilf}}
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