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A020964
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Sum of Floor[ 3*(1+sqrt(2))^(n-k) ] for k from 1 to infinity.
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1
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4, 11, 28, 70, 171, 417, 1010, 2444, 5905, 14263, 34440, 83154, 200759, 484685, 1170142, 2824984, 6820125, 16465251, 39750644, 95966558, 231683779, 559334137, 1350352074, 3260038308, 7870428713, 19000895759
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OFFSET
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1,1
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LINKS
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C. Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.
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MATHEMATICA
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Table[t=0; k=0; While[k++; s=Floor[3*(1+Sqrt[2])^(n-k)]; s>0, t= t+s]; t, {n, 26}]
Table[Sum[Floor[3*(1+Sqrt[2])^(n-k)], {k, 1, 1000}], {n, 0, 50}] (* G. C. Greubel, Sep 30 2018 *)
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PROG
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(PARI) for(n=1, 50, print1(sum(k=1, 2*n, floor(3*(1+sqrt(2))^(n-k))), ", ")) \\ G. C. Greubel, Sep 30 2018
(Magma) [(&+[Floor(3*(1+sqrt(2))^(n-k)): k in [1..2*n]]): n in [1..50]] // G. C. Greubel, Sep 30 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Revised Feb 03 1999. Revised Nov 30 2010.
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STATUS
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approved
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