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A060816
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a(n)=3*a(n-1) + 1; a(0)=1, a(1)=2.
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10
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1, 2, 7, 22, 67, 202, 607, 1822, 5467, 16402, 49207, 147622, 442867, 1328602, 3985807, 11957422, 35872267, 107616802, 322850407, 968551222, 2905653667, 8716961002, 26150883007, 78452649022, 235357947067, 706073841202
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| From Erich Friedman's math magic page 2nd paragraph under "Answers" section.
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=2,(i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=(-1)^n*charpoly(A,-1). [From Milan R. Janjic (agnus(AT)blic.net), Jan 26 2010]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
Erich Friedman, Math. Magic
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FORMULA
| For n>0: a(n) = (5*3^(n-1)-1)/2 = a(n-1)+5*3^(n-2) = (5*A003462(n)+1)/3 = a(n-1)+A005030(n-2) - Henry Bottomley (se16(AT)btinternet.com), May 01 2001
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PROG
| (PARI) { for (n=0, 200, if (n>1, a1=a=3*a1 + 1, if (n==0, a=1, a1=a=2)); write("b060816.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 13 2009]
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CROSSREFS
| Equals A057198 - 1.
Sequence in context: A084264 A088211 A071684 * A171847 A037552 A094618
Adjacent sequences: A060813 A060814 A060815 * A060817 A060818 A060819
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Apr 29 2001
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