A129231 a(n) = floor(n*r) - a(n-1), where r = sqrt(2) and a(0) = 0.

0, 1, 1, 3, 2, 5, 3, 6, 5, 7, 7, 8, 8, 10, 9, 12, 10, 14, 11, 15, 13, 16, 15, 17, 16, 19, 17, 21, 18, 23, 19, 24, 21, 25, 23, 26, 24, 28, 25, 30, 26, 31, 28, 32, 30, 33, 32, 34, 33, 36, 34, 38, 35, 39, 37, 40, 39, 41, 41, 42, 42, 44, 43, 46, 44, 47, 46, 48, 48, 49, 49, 51, 50, 53

Offset

0,4

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Formula

a(n) = floor(n*r) - floor((n-1)*r) + floor((n-2)*r) - ... + d*floor(r), where d = (-1)^(n+1) and r = sqrt(2).

Mathematica

Block[{n = 0}, NestList[Floor[++n*Sqrt[2]] - # &, 0, 100]] (* Paolo Xausa, May 11 2024 *)

Crossrefs

Cf. A129229, A129232.

Sequence in context: A247815 A057953 A372679 * A166477 A124332 A364900

Adjacent sequences: A129228 A129229 A129230 * A129232 A129233 A129234

Keyword

nonn

Author

Clark Kimberling, Apr 04 2007

Extensions

a(47) corrected by Georg Fischer, May 11 2024

Status

approved