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Search: id:A137241
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| A137241 |
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Number triples (k,3-k,2-2k), concatenated for k=0, 1, 2, 3,... |
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+0
5
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| 0, 3, 2, 1, 2, 0, 2, 1, -2, 3, 0, -4, 4, -1, -6, 5, -2, -8, 6, -3, -10, 7, -4, -12, 8, -5, -14, 9, -6, -16, 10, -7, -18, 11, -8, -20, 12, -9, -22, 13, -10, -24, 14, -11, -26, 15, -12, -28, 16, -13, -30, 17, -14, -32, 18, -15, -34, 19, -16, -36, 20, -17, -38, 21, -18, -40
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The entries are the coefficients in a family of Jacobsthal recurrences: a(n)=k*a(n-1)+(3-k)*a(n-2)+(2-2k)*a(n-3).
Examples for k=0 are in A001045 and A113954. Examples for k=1 are A001045, A078008.
Examples for k=2 are A000975, A087288, A084639, A000012 and A001045.
Examples for k=3 are A045883, A059570. Examples for k=4 are A094705 and A015518.
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FORMULA
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a(n)=2*a(n-3)-a(n-6). G.f.: x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x+x^2)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 25 2009]
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EXAMPLE
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The triples (k,3-k,2-2k) are (0,3,2), (1,2,0), (2,1,-2), (3,0,-4),...
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CROSSREFS
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Sequence in context: A101479 A136170 A101221 this_sequence A016457 A077089 A156352
Adjacent sequences: A137238 A137239 A137240 this_sequence A137242 A137243 A137244
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KEYWORD
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easy,sign,less
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Mar 09 2008
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 28 2008
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