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A083579
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Generalized Jacobsthal numbers.
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4
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0, 1, 1, 4, 8, 19, 39, 82, 166, 337, 677, 1360, 2724, 5455, 10915, 21838, 43682, 87373, 174753, 349516, 699040, 1398091, 2796191, 5592394, 11184798, 22369609, 44739229, 89478472, 178956956, 357913927, 715827867, 1431655750, 2863311514
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(n) = 2*2^n/3-5*(-1)^n/12-(2*n+1)/4.
a(n+2) = a(n+1)+2*a(n)+n, a(0)=0, a(1)=1.
G.f.: x*(1-2*x+2*x^2)/(1-3*x+x^2+3*x^3-2*x^4). [Colin Barker, Jan 16 2012]
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=b+2*a+n; a=b; b=c, {n, 0, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 21 2011*)
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CROSSREFS
| Cf. A083580.
Sequence in context: A049933 A163318 A129362 * A065034 A178447 A006580
Adjacent sequences: A083576 A083577 A083578 * A083580 A083581 A083582
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 01 2003
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