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Search: id:A078140
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| A078140 |
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Convolutory inverse of signed lower Wythoff sequence. |
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+0
1
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| 1, 3, 5, 9, 17, 30, 52, 90, 154, 262, 446, 758, 1285, 2176, 3683, 6230, 10533, 17803, 30085, 50831, 85873, 145063, 245037, 413891, 699082, 1180761, 1994293, 3368302, 5688920, 9608292, 16227841, 27407792, 46289925, 78180465, 132041227
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = d*[w(n)*a(1)-w(n-1)*a(2)+...+d*w(2)*a(n-1)], where d=(-1)^n, with a(1)=1, and w=Floor(n*tau), tau=(1+sqrt(5))/2.
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EXAMPLE
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a(5) = 17 = -[w(5)*a(1)-w(4)*a(2)+w(3)*a(3)-w(2)*a(4)] = -8*1+6*3-4*5+3*9. (a(1),a(2),...,a(n))(*)(w(1),-w(2),w(3),...,-d*w(n)) = (1,0,0,...,0), where (*) denotes convolution, w = lower Wythoff sequence, A000201.
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CROSSREFS
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Cf. A000201, A077607.
Adjacent sequences: A078137 A078138 A078139 this_sequence A078141 A078142 A078143
Sequence in context: A032679 A018162 A077879 this_sequence A102475 A066173 A114322
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Nov 23 2002
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