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

+0
3

0, 1, 2, 4, 6, 6, 9, 12, 12, 12, 16, 20, 20, 20, 20, 25, 30, 30, 30, 30, 30, 36, 42, 42, 42, 42, 42, 42, 49, 56, 56, 56, 56, 56, 56, 56, 64, 72, 72, 72, 72, 72, 72, 72, 72, 81, 90, 90, 90, 90, 90, 90, 90, 90, 90, 100, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 121 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`m^2 (when n is m-th triangular number) followed by m copies of m-th pronic [m(m+1)].`
	FORMULA	`a(n) =floor[(sqrt(8n+1)-1)/2]ceiling[(sqrt(8n+1)-1)/2] =A002024(n)A003056(n) =A056943(n)+n =2n-A056944(n). If n=t(t+1)/2 then a(n)=t^2; if t(t-1)/2<n<t(t+1)/2 then a(n)=t(t-1).`
	EXAMPLE	`a(9)=12 since spiral is as marked by 9 X's in 4*3=12 rectangle:` `X.XX` `X..X` `XXXX`
	CROSSREFS	`Cf. A000217, A000290, A002024, A002378, A002620, A003056, A038759, A056943, A056944.` `Adjacent sequences: A056939 A056940 A056941 this_sequence A056943 A056944 A056945` `Sequence in context: A023853 A056526 A049066 this_sequence A115947 A061228 A070229`
	KEYWORD	`easy,nice,nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Jul 13 2000`

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Last modified October 10 20:39 EDT 2008. Contains 144831 sequences.

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