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Search: id:A138110
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| A138110 |
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Table T(d,n) read column by column: the n-th term in the sequence of the d-th differences of A138112, d=0..4. |
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+0
2
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| 0, 0, 0, 1, -1, 0, 0, 1, 0, -1, 0, 1, 1, -1, -1, 1, 2, 0, -2, -1, 3, 2, -2, -3, 0, 5, 0, -5, -3, 3, 5, -5, -8, 0, 8, 0, -13, -8, 8, 13, -13, -21, 0, 21, 13, -34, -21, 21, 34, 0, -55, 0, 55, 34, -34, -55, 55, 89, 0, -89, 0, 144, 89, -89, -144, 144, 233, 0, -233, -144, 377, 233, -233, -377, 0, 610, 0, -610, -377, 377
(list; graph; listen)
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OFFSET
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0,17
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COMMENT
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Ignoring signs, the sequence contains A000045(2)=1 ten times and each of the following Fibonacci numbers A000045(i>2) four times.
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FORMULA
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T(0,n)=A138112(n). T(d,n)= T(d-1,n+1)-T(d-1,n), d=1..4.
T(1,n)=A100334(n-1). T(2,n)=A103311(n). T(3,n) = -A138003(n-2). T(4,n)= -A105371(n).
sum_(d=0..4) T(d,n)=0 (columns sum to zero).
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EXAMPLE
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All 5 rows of the table T(d,n) are:
.0,.0,.0,.1,.3,.5,.5,..0,-13,-34,-55,-55,...0,.144,...
.0,.0,.1,.2,.2,.0,-5,-13,-21,-21,..0,.55,.144,.233,...
.0,.1,.1,.0,-2,-5,-8,.-8,..0,.21,.55,.89,..89,...0,...
.1,.0,-1,-2,-3,-3,.0,..8,.21,.34,.34,..0,.-89,-233,...
-1,-1,-1,-1,.0,.3,.8,.13,.13,..0,-34,-89,-144,-144,...
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CROSSREFS
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Cf. A102312 (A049666), A099100, A134489, A134490, A134491.
Sequence in context: A029184 A029221 A029183 this_sequence A080233 A156644 A097808
Adjacent sequences: A138107 A138108 A138109 this_sequence A138111 A138112 A138113
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KEYWORD
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sign,tabf,less
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 04 2008
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 04 2008
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