A020958 a(n) = Sum_{k >= 1} floor(3*tau^(n-k)).

5, 9, 16, 28, 48, 81, 134, 221, 361, 589, 957, 1554, 2519, 4082, 6610, 10702, 17322, 28035, 45368, 73415, 118795, 192223, 311031, 503268, 814313, 1317596, 2131924, 3449536, 5581476, 9031029, 14612522, 23643569, 38256109, 61899697, 100155825, 162055542, 262211387

Offset

1,1

Comments

Since 3*tau^(-3) < 1 the number of nonzero terms in the sum is finite. - Giovanni Resta, Jul 08 2019

Links

Table of n, a(n) for n=1..37.

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

Formula

a(n) = Sum_{k=-2..(n-1)} floor(3*tau^k). - Giovanni Resta, Jul 08 2019

Mathematica

a[n_] := Sum[Floor[3 GoldenRatio^k], {k, -2, n-1}]; Array[a, 37] (* Giovanni Resta, Jul 08 2019 *)

Crossrefs

Cf. A001622 (tau), A020957.

Sequence in context: A356675 A072174 A188555 * A020750 A020713 A090990

Adjacent sequences: A020955 A020956 A020957 * A020959 A020960 A020961

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Michel Marcus, Jul 06 2019

a(27)-a(37) from Giovanni Resta, Jul 08 2019

Status

approved