A068908 - OEIS

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A068908

Number of partitions of n modulo 5.

1, 1, 2, 3, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 3, 1, 0, 3, 0, 4, 2, 4, 3, 0, 3, 2, 2, 0, 0, 3, 3, 4, 1, 0, 4, 3, 4, 3, 0, 1, 3, 4, 1, 0, 1, 3, 4, 0, 0, 2, 0, 1, 4, 0, 3, 0, 4, 0, 0, 3, 0, 3, 4, 0, 4, 1, 3, 4, 0, 1, 2, 0, 4, 0, 2, 2, 3, 4, 0, 3, 4, 2, 2, 0, 4, 4, 0, 1, 0, 2, 1, 4, 0, 0 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`Of the partitions of numbers from 1 to 100000: 36256 are 0, 15758 are 1, 16133 are 2, 16028 are 3 and 15825 are 4 modulo 5, largely because the number of partitions of 5m+4 is always a multiple of 5.`
	LINKS	`Henry Bottomley, Partition calculators using java applets` `Index entries for sequences related to partitions`
	FORMULA	`a(n) =A010874(A000041(n)) =A068906(5, n)` `a(n) = Pm(n,1) with Pm(n,k) = if k<n then (Pm(n-k,k) + Pm(n,k+1)) mod 5 else 0^(n*(k-n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 09 2009]`
	CROSSREFS	`Cf. A040051, A068907, A068909, A020919.` `Sequence in context: A059067 A065861 A126832 * A113407 A039703 A171935` `Adjacent sequences: A068905 A068906 A068907 * A068909 A068910 A068911`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Mar 05 2002`

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Last modified February 14 05:41 EST 2012. Contains 205570 sequences.