id:A064173 - OEIS Search Results

Search: id:A064173

Displaying 1-1 of 1 results found.

page 1

Number of partitions of n with positive rank.

+0
7

0, 1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 80, 106, 136, 178, 225, 291, 366, 466, 583, 735, 912, 1140, 1407, 1743, 2140, 2634, 3214, 3932, 4776, 5807, 7022, 8495, 10225, 12313, 14762, 17696, 21136, 25236, 30030, 35722, 42367, 50216, 59368, 70138 (list; graph; listen)

	OFFSET	`1,4`
	COMMENT	`The rank of a partition is the largest summand minus the number of summands.`
	FORMULA	`a(n) = (A000041(n)-A047993(n))/2.` `a(n) = p(n-2)-p(n-7)+p(n-15)-... -(-1)^kp(n-(3k^2+k)/2)+..., where p() is A000041(). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 04 2004`
	EXAMPLE	`a(20) = p(18)-p(13)+p(5) =385-101+7 = 291.`
	MAPLE	`with(combinat): for n from 1 to 30 do P:=partition(n): c:=0: for j from 1 to nops(P) do if P[j][nops(P[j])]>nops(P[j]) then c:=c+1 else c:=c fi od: a[n]:=c: od: seq(a[n], n=1..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 11 2004`
	CROSSREFS	`Cf. A063995.` `Cf. A064174.` `Sequence in context: A027339 A039837 A039838 this_sequence A039843 A045880 A014853` `Adjacent sequences: A064170 A064171 A064172 this_sequence A064174 A064175 A064176`
	KEYWORD	`nonn`
	AUTHOR	`Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 19 2001`

page 1

Search completed in 0.002 seconds

Last modified September 5 01:44 EDT 2008. Contains 143476 sequences.

AT&T Labs Research