id:A056943 - OEIS Search Results

Search: id:A056943

Displaying 1-1 of 1 results found.

page 1

Unused area of rectangle needed to enclose a non-touching spiral of length n on a square lattice.

+0
3

0, 0, 0, 1, 2, 1, 3, 5, 4, 3, 6, 9, 8, 7, 6, 10, 14, 13, 12, 11, 10, 15, 20, 19, 18, 17, 16, 15, 21, 27, 26, 25, 24, 23, 22, 21, 28, 35, 34, 33, 32, 31, 30, 29, 28, 36, 44, 43, 42, 41, 40, 39, 38, 37, 36, 45, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 55, 65, 64, 63, 62, 61, 60, 59 (list; graph; listen)

	OFFSET	`0,5`
	FORMULA	`a(n) =floor[(sqrt(8n+1)-1)/2]ceiling[(sqrt(8n+1)-1)/2]-n =A002024(n)A003056(n)-n =A056942(n)-n =n-A056944(n). If n=t(t+1)/2 then a(n)=t(t-1)/2; if n=t(t+1)/2+k with 0<k <= t then a(n)=t(t+1)/2-k.`
	EXAMPLE	`a(9)=3 since spiral is as marked by 9 X's in 4*3=12 rectangle, with 12-9=3 spaces unused:` `X.XX` `X..X` `XXXX`
	CROSSREFS	`Cf. A002024, A003056, A056942, A056944.` `Adjacent sequences: A056940 A056941 A056942 this_sequence A056944 A056945 A056946` `Sequence in context: A019588 A060083 A069931 this_sequence A064429 A113790 A063705`
	KEYWORD	`easy,nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Jul 13 2000`

page 1

Search completed in 0.002 seconds

Last modified May 16 01:24 EDT 2008. Contains 139630 sequences.

AT&T Labs Research