A191402 a(n) = A000201(n) + A000201(n+1).

1, 4, 7, 10, 14, 17, 20, 23, 26, 30, 33, 36, 40, 43, 46, 49, 52, 56, 59, 62, 65, 68, 72, 75, 78, 82, 85, 88, 91, 94, 98, 101, 104, 108, 111, 114, 117, 120, 124, 127, 130, 133, 136, 140, 143, 146, 150, 153, 156, 159, 162, 166, 169, 172, 175, 178, 182, 185, 188, 192, 195, 198, 201, 204, 208, 211, 214, 218, 221, 224

Offset

0,2

Links

Table of n, a(n) for n=0..69.

Formula

a(n) = [nr] + [nr+r], where r=(1+sqrt(5))/2 and [ ]=floor.

Mathematica

r = GoldenRatio; f[n_] := Floor[n*r];
Table[f[n]+f[n+1], {n, 0, 100}]
(* A191402(n)=A000201(n)+A000201(n+1) *)
Table[f[n] + f[n+2], {n, 0, 100}]
(* A191403(n)=A000201(n)+A000201(n+2) *)
Table[f[n] + f[n+3], {n, 0, 100}]
(* A191404(n)=A000201(n)+A000201(n+3) *)

Prog

(Python)
from math import isqrt
def A191402(n): return (n+isqrt(m:=5*n**2)>>1)+(n+1+isqrt(m+10*n+5)>>1) # Chai Wah Wu, Aug 10 2022

Crossrefs

Cf. A191403, A191404.

Sequence in context: A310687 A310688 A062389 * A080600 A198266 A067497

Adjacent sequences: A191399 A191400 A191401 * A191403 A191404 A191405

Keyword

nonn

Author

Clark Kimberling, Jun 01 2011

Status

approved