A020964 - OEIS

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A020964

Sum of Floor[ 3*(1+sqrt(2))^(n-k) ] for k from 1 to infinity.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

C. Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A339252 A005409 A245124 * A113067 A290890 A152689

Adjacent sequences: A020961 A020962 A020963 * A020965 A020966 A020967

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Revised Feb 03 1999. Revised Nov 30 2010.

STATUS

approved