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A083101
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a(n)=2a(n-1)+10a(n-2).
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2
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1, 12, 34, 188, 716, 3312, 13784, 60688, 259216, 1125312, 4842784, 20938688, 90305216, 389997312, 1683046784, 7266066688, 31362601216, 135385869312, 584397750784, 2522654194688, 10889285897216, 47005113741312
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n+1)=a(n)+11*A083102(n). a(n)/A083102(n) converges to sqrt(11).
a(n-1) is the number of compositions of n when there are 1 type of 1 and 11 types of other natural numbers. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
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FORMULA
| G.f.: (1+10x)/(1-2x-10x^2)
a(n)=(1/2)*[1+sqrt(11)]^n-(1/2)*sqrt(11)*[1-sqrt(11)]^n+(1/2)*[1-sqrt(11)]^n+(1/2)*[1 +sqrt(11)]^n*sqrt(11), with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 10 2008
If p[1]=1, and p[i]=11,(i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=det A. [From Milan R. Janjic (agnus(AT)blic.net), Apr 29 2010]
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MATHEMATICA
| CoefficientList[Series[(1+10x)/(1-2x-10x^2), {x, 0, 25}], x]
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CROSSREFS
| Sequence in context: A078194 A034510 * A133294 A082240 A088596 A077293
Adjacent sequences: A083098 A083099 A083100 * A083102 A083103 A083104
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Apr 22 2003
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