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A141685
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An Invert transform sequence of the form: a(n)=Sum[Mod[k,3]*a(n-k),{k,1,n}].
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0
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1, 1, 3, 5, 12, 25, 54, 116, 249, 535, 1149, 2468, 5301, 11386, 24456, 52529, 112827, 242341, 520524, 1118033, 2401422, 5158012, 11078889, 23796335, 51112125, 109783684, 235804269, 506483762, 1087875984, 2336647777, 5018883507
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Limit[a(n+1)/a(n),n->Infinity]=2.1478990357047874
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FORMULA
| a(n)=Sum[Mod[k,3]*a(n-k),{k,1,n}].
If p[i]=modp(i,3) 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), May 02 2010]
Empirical G.f.: x*(1-x)*(1+x+x^2)/(1-x-2*x^2-x^3). [Colin Barker, Feb 01 2012]
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MATHEMATICA
| a[0] = 1; a[n_] := a[n] = Sum[Mod[k, 3]*a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]
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CROSSREFS
| Sequence in context: A030270 A129757 A135019 * A017921 A161762 A005913
Adjacent sequences: A141682 A141683 A141684 * A141686 A141687 A141688
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KEYWORD
| nonn,uned,changed
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 08 2008
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