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Search: id:A140991
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| A140991 |
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(1/9)*(7*2^n+(-1)^n*(3*n+2))-(n-1)^2. |
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+0
1
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| 0, 1, 3, 1, 5, 7, 27, 61, 153, 331, 719, 1489, 3069, 6223, 12579, 25285, 50753, 101683, 203607, 407449, 815205, 1630711, 3261803, 6523981, 13048425, 26097307, 52195167, 104390881
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1990, p. 327.
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FORMULA
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a(n)=3a(n-1)-6 a(n-3) +3a(n-4) +3a(n-5) -2a(n-6). G.f.: x*(1-8*x^2+8*x^3+7*x^4)/((-1+2*x)*(1+x)^2*(x-1)^3) . [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 27 2009]
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EXAMPLE
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If n=0, then a(0)=1/9*(7*2^0+(-1)^0*(3*0+2))-(0-1)^2=1/9*(7*1+1*(0+2))-(-1)^2 =1/9*(7+1*2)-1=1/9*(7+2)-1=(1/9)*9-1=1-1=0
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CROSSREFS
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Cf. A006904. a(n) = A006904(n)-(n-1)^2.
Sequence in context: A049764 A136437 A137328 this_sequence A038738 A116647 A063858
Adjacent sequences: A140988 A140989 A140990 this_sequence A140992 A140993 A140994
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 08 2008
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EXTENSIONS
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Definition corrected by D. S. McNeil (d.mcneil(AT)qmul.ac.uk), Mar 21 2009
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