A056943 - OEIS

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A056943

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

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; refs; listen; history; text; internal format)

	OFFSET	`0,5`
	LINKS	`Table of n, a(n) for n=0..73.`
	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.` `Sequence in context: A209135 A209139 A182939 * A171085 A064429 A113790` `Adjacent sequences: A056940 A056941 A056942 * A056944 A056945 A056946`
	KEYWORD	`easy,nonn`
	AUTHOR	`Henry Bottomley, Jul 13 2000`
	STATUS	`approved`

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Last modified May 24 00:43 EDT 2013. Contains 225613 sequences.