id:A068909 - OEIS Search Results

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Number of partitions of n modulo 7.

+0
4

1, 1, 2, 3, 5, 0, 4, 1, 1, 2, 0, 0, 0, 3, 2, 1, 0, 3, 0, 0, 4, 1, 1, 2, 0, 5, 0, 0, 1, 1, 4, 3, 5, 0, 4, 1, 1, 0, 3, 0, 0, 0, 2, 2, 2, 3, 5, 0, 0, 2, 1, 4, 0, 0, 0, 0, 3, 2, 2, 3, 5, 0, 4, 2, 2, 2, 3, 5, 0, 4, 3, 2, 4, 6, 5, 0, 0, 2, 2, 4, 3, 5, 0, 0, 3, 3, 6, 6, 3, 0, 1, 3, 3, 4, 3, 5, 0, 0, 4, 3, 4, 6, 5, 0, 1 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`Of the partitions of numbers from 1 to 100000: 27193 are 0, 12078 are 1, 12203 are 2, 12260 are 3, 12231 are 4, 12003 are 5 and 12032 are 6 modulo 7, largely because the number of partitions of 7m+5 is always a multiple of 7.`
	LINKS	`Henry Bottomley, Partition calculators using java applets` `Index entries for sequences related to partitions`
	FORMULA	`a(n) =A010876(A000041(n)) =A068906(7, n)` `a(n) = Pm(n,1) with Pm(n,k) = if k<n then (Pm(n-k,k) + Pm(n,k+1)) mod 7 else 0^(n*(k-n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 09 2009]`
	CROSSREFS	`Cf. A040051, A068907, A068908, A020919.` `Sequence in context: A024595 A144804 A118308 this_sequence A039705 A082118 A079344` `Adjacent sequences: A068906 A068907 A068908 this_sequence A068910 A068911 A068912`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Mar 05 2002`

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Last modified November 29 12:46 EST 2009. Contains 167659 sequences.

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