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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
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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, 208782413, 417565471, 835131699, 1670264149
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1990, p. 327.
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FORMULA
| a(n) = A006904(n)-(n-1)^2.
a(n) = 3*a(n-1) -6*a(n-3) +3*a(n-4) +3*a(n-5) -2*a(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
| 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+2)-1 = 1-1 = 0.
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PROG
| (MAGMA) [ (1/9)*(7*2^n+(-1)^n*(3*n+2))-(n-1)^2: n in [0..100] ]; [From Vincenzo Librandi, Dec 19 2010]
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CROSSREFS
| Cf. A006904.
Sequence in context: A049764 A136437 A137328 * A038738 A116647 A063858
Adjacent sequences: A140988 A140989 A140990 * A140992 A140993 A140994
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KEYWORD
| nonn
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 08 2008
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EXTENSIONS
| Definition corrected by D. S. McNeil (d.mcneil(AT)qmul.ac.uk), Mar 21 2009
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