id:A059512 - OEIS Search Results

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For n>=2, the number of (s(0), s(1), ..., s(n-1)) such that 0 < s(i) < 5 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n-1, s(0) = 2, s(n-1) = 2.

+0
5

0, 1, 1, 3, 7, 18, 46, 119, 309, 805, 2101, 5490, 14356, 37557, 98281, 257231, 673323, 1762594, 4614226, 12079707, 31624285, 82792161, 216750601, 567457058, 1485616392, 3889385353, 10182528721, 26658183099, 69791991919 (list; graph; listen)

	OFFSET	`0,4`
	COMMENT	`Substituting x(1-x)/(1-2x) into x/(1-x^2) yields g.f. of sequence.`
	FORMULA	`a(n) = 2a(n-1) + Sum{m<n-1}a(m) - F(n-3) where F(n) is the n-th Fibonacci number (A000045).` `G.f.: x(1-x)(1-2x)/((1-x-x^2)(1-3x+x^2)).`
	PROGRAM	`(PARI) a(n)=(fibonacci(2*n-1)+fibonacci(n-2))/2`
	CROSSREFS	`Cf. A000667, A059216, A059219, A059502, A027994.` `a(1-2n)=A005207(2n), a(-2n)=A056014(2n+1).` `Sequence in context: A116413 A078058 A052960 this_sequence A094297 A026107 A027969` `Adjacent sequences: A059509 A059510 A059511 this_sequence A059513 A059514 A059515`
	KEYWORD	`easy,nonn`
	AUTHOR	`Floor van Lamoen (fvlamoen(AT)hotmail.com), Jan 21 2001`

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Last modified December 2 15:58 EST 2008. Contains 150992 sequences.

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