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Search: id:A115032
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| A115032 |
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Expansion of (5-14*x+x^2)/((1-x)*(x^2-18*x+1)); relates squares of numerators and denominators of continued fraction convergents to sqrt(5). |
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1
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| 5, 81, 1445, 25921, 465125, 8346321, 149768645, 2687489281, 48225038405, 865363202001, 15528312597605, 278644263554881, 5000068431390245, 89722587501469521, 1610006506595061125, 28890394531209630721
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Sequence is generated by the floretion A*B*C with A = + 'i - 'k + i' - k' - 'jj' - 'ij' - 'ji' - 'jk' - 'kj' ; B = - 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj' ; C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' (apart from a factor (-1)^n)
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FORMULA
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sqrt(a(2n)) = sqrt(5)*A007805(n) = sqrt(5)*Fib(6n+3)/2 = sqrt(5)*A001076(2n+1). sqrt(a(2n+1)) = A023039(2n+1) = A001077(2n).
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PROGRAM
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Floretion Algebra Multiplciation Program, FAMP Code: tesseq[A*B*C] (see comment).
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CROSSREFS
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Cf. A001076, A001077, A007805, A023039, A097924.
Sequence in context: A062364 A110257 A135918 this_sequence A009733 A009756 A009634
Adjacent sequences: A115029 A115030 A115031 this_sequence A115033 A115034 A115035
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KEYWORD
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easy,nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Feb 26 2006
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