A020963 Sum of Floor[ 2*(1+sqrt(2))^(n-k) ] for k from 1 to infinity.

2, 6, 17, 45, 112, 276, 671, 1627, 3934, 9506, 22957, 55433, 133836, 323120, 780091, 1883319, 4546746, 10976830, 26500425, 63977701, 154455848, 372889420, 900234711, 2173358867, 5246952470, 12667263834

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.

Formula

From Chai Wah Wu, Jun 02 2016: (Start)

a(n) = 3*a(n-1) - 4*a(n-3) + a(n-4) + a(n-5) for n > 5 (conjectured).

G.f.: x*(x^4 - 2*x^3 + x^2 - 2)/((x - 1)^2*(x + 1)*(x^2 + 2*x - 1)) (conjectured). (End)

Mathematica

Table[t=0; k=0; While[k++; s=Floor[2*(1+Sqrt[2])^(n-k)]; s>0, t=t+s]; t, {n, 26}]
Table[Sum[Floor[2*(1 + Sqrt[2])^(n - k)], {k, 1, 1000}], {n, 1, 50}] (* G. C. Greubel, Sep 30 2018 *)

Prog

(PARI) for(n=1, 50, print1(sum(k=1, 2*n, floor(2*(1+sqrt(2))^(n-k))), ", ")) \\ G. C. Greubel, Sep 30 2018
(Magma) [(&+[Floor(2*(1+sqrt(2))^(n-k)): k in [1..2*n]]): n in [1..50]] // G. C. Greubel, Sep 30 2018

Crossrefs

Sequence in context: A190159 A000996 A309757 * A065068 A109961 A288029

Adjacent sequences: A020960 A020961 A020962 * A020964 A020965 A020966

Keyword

nonn

Author

Clark Kimberling

Extensions

Revised Feb 03 1999. Revised Nov 30 2010.

Status

approved