id:A056944 - OEIS Search Results

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Amount by which used area of rectangle needed to enclose a non-touching spiral of length n on a square lattice exceeds unused area.

+0
5

0, 1, 2, 2, 2, 4, 3, 2, 4, 6, 4, 2, 4, 6, 8, 5, 2, 4, 6, 8, 10, 6, 2, 4, 6, 8, 10, 12, 7, 2, 4, 6, 8, 10, 12, 14, 8, 2, 4, 6, 8, 10, 12, 14, 16, 9, 2, 4, 6, 8, 10, 12, 14, 16, 18, 10, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 11, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 12, 2, 4, 6, 8, 10, 12, 14, 16 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`m (when n is m-th triangular number) followed by m even numbers from 2 through 2m.`
	FORMULA	`a(n) =2n-floor[(sqrt(8n+1)-1)/2]ceiling[(sqrt(8n+1)-1)/2] =2n-A002024(n)A003056(n) =2n-A056942(n) =n-A056943(n). If n=t(t+1)/2 then a(n)=t; if n=t(t+1)/2+k with 0<k <= t then a(n)=2k.`
	EXAMPLE	`a(9)=6 since spiral is as marked by 9 X's in 4*3=12 rectangle, with 12-9=3 spaces unused, and a used-unused difference of 9-3=6:` `X.XX` `X..X` `XXXX`
	CROSSREFS	`Cf. A002024, A003056, A056942, A056943.` `Sequence in context: A064025 A054709 A121806 this_sequence A050493 A085454 A083403` `Adjacent sequences: A056941 A056942 A056943 this_sequence A056945 A056946 A056947`
	KEYWORD	`easy,nonn,nice`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Jul 13 2000`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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