A020962 a(n) = Sum_{k >= 1} floor((1+sqrt(2))^(n-k)).

1, 3, 8, 22, 55, 137, 334, 812, 1965, 4751, 11476, 27714, 66915, 161557, 390042, 941656, 2273369, 5488411, 13250208, 31988846, 77227919, 186444705, 450117350, 1086679428, 2623476229, 6333631911, 15290740076

Offset

1,2

Links

Table of n, a(n) for n=1..27.

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

Formula

a(n) = Sum_{i=0..n-1} A080039(i).

Mathematica

Table[Sum[Floor[(1 + Sqrt[2])^(n - k)], {k, Infinity}], {n, 1, 27}] (* Alonso del Arte, Nov 30 2010 *)

Crossrefs

Cf. A080039.

Sequence in context: A027235 A086596 A036882 * A027243 A110239 A271893

Adjacent sequences: A020959 A020960 A020961 * A020963 A020964 A020965

Keyword

nonn

Author

Clark Kimberling

Extensions

Revised Feb 03 1999. Revised Nov 30 2010.

Status

approved