A106791 - OEIS

This site is supported by donations to The OEIS Foundation.

A106791

Sum of two consecutive squares of Lucas 4-step numbers (A073817).

17, 10, 58, 274, 901, 3277, 12402, 46282, 171170, 635953, 2364489, 8785386, 32637202, 121265666, 450571589, 1674090725, 6220049810, 23110593298, 85867345570, 319039636721, 1185390110881, 4404311472106, 16364198176874 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,1`
	COMMENTS	`A106729 is sum of two consecutive squares of Lucas numbers (A001254), for which L(n)^2 + L(n+1)^2 = 5{F(n)^2 + F(n+1)^2} = 5A001519(n). Axxxxxx is sum of two consecutive squares of Lucas 3-step numbers (A001644). Sum of two consecutive squares of Lucas 4-step numbers can be expressed in terms of tetranacci numbers, but not quite as neatly.`
	FORMULA	`a(n) = A073817(n)^2 + A073817(n+1)^2. a(n) = 5A073817(n)^2 + 4A073817(n)*A073817(n-4) + A073817(n-4)^2.`
	EXAMPLE	`a(0) = A073817(0)^2 + A073817(1)^2 = 4^2 + 1^2 = 16 + 1 = 17.` `a(1) = A073817(1)^2 + A073817(2)^2 = 1^2 + 3^2 = 1 + 9 = 10.` `a(2) = A073817(2)^2 + A073817(3)^2 = 3^2 + 7^2 = 9 + 49 = 58.` `a(3) = A073817(3)^2 + A073817(4)^2 = 7^2 + 15^2 = 49 + 225 = 274.` `a(4) = A073817(4)^2 + A073817(5)^2 = 15^2 + 26^2 = 225 + 676 = 901 = 30^2 + 1.` `a(5) = A073817(5)^2 + A073817(6)^2 = 26^2 + 51^2 = 676 + 2601 = 3277.`
	CROSSREFS	`Cf. A073817, A106729.` `Sequence in context: A113779 A061049 A166524 * A040274 A164064 A073887` `Adjacent sequences: A106788 A106789 A106790 * A106792 A106793 A106794`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), May 16 2005`

Content is available under The OEIS End-User License Agreement .

Last modified February 17 00:09 EST 2012. Contains 205978 sequences.