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A062092
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a(n)=2*a(n-1)-(-1)^n, a(0)=2.
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8
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2, 5, 9, 19, 37, 75, 149, 299, 597, 1195, 2389, 4779, 9557, 19115, 38229, 76459, 152917, 305835, 611669, 1223339, 2446677, 4893355, 9786709, 19573419, 39146837, 78293675, 156587349, 313174699, 626349397, 1252698795, 2505397589
(list;
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refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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Let A be the Hessenberg matrix of order n, defined by: A[1,j]=A[i,i]:=1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=charpoly(A,3). [From Milan Janjic, Jan 24 2010]
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REFERENCES
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T. Koshy, Fibonacci and Lucas numbers with applications, Wiley, 2001, p. 98.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
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a(n)=a(n-1)+2*a(n-2)=(7*2^n-(-1)^n)/3.
G.f.: (2+3*x)/(1-x-2*x^2). E.g.f.: (7*exp(2*x)-exp(-x))/3.
Running sum of 3 consecutive elements of Jacobsthal sequence A001045(n): a(n) = A001045(n) + A001045(n-1) + A001045(n-2). - Alexander Adamchuk, May 16 2006
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EXAMPLE
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a(4) = 37 hence a(5) = 2*37 + 1=75 and a(6) = 2*75 - 1 = 149.
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MATHEMATICA
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f1[n_]:=2*n+1; f2[n_]:=2*n-1; a=2; lst={a}; Do[AppendTo[lst, a=f1[a]]; AppendTo[lst, a=f2[a]], {n, 30}]; lst [From Vladimir Joseph Stephan Orlovsky, Feb 07 2010]
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PROG
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(PARI) { for (n=0, 200, write("b062092.txt", n, " ", (7*2^n - (-1)^n)/3) ) } [From Harry J. Smith, Aug 01 2009]
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CROSSREFS
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Cf. A062092(n)=2^(n+1)+A001045(n). A002487(A062092(n))=A000032(n+1).
Cf. A001045.
Sequence in context: A122893 A178841 A214319 * A079117 A030137 A105309
Adjacent sequences: A062089 A062090 A062091 * A062093 A062094 A062095
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KEYWORD
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nonn,easy
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 16 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jun 18 2001
Additional comments from Michael Somos, Jun 24 2002
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STATUS
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approved
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