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

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: A018024 A190159 A000996 * 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

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Last modified March 25 02:31 EDT 2019. Contains 321450 sequences. (Running on oeis4.)