A371382 a(n) = n^2 + q*(q + 1), where q = floor(n*(1 + sqrt(5))/2) = A000201(n).

3, 16, 29, 58, 97, 126, 181, 220, 291, 372, 427, 524, 631, 702, 825, 906, 1045, 1194, 1291, 1456, 1563, 1744, 1935, 2058, 2265, 2482, 2621, 2854, 3003, 3252, 3511, 3676, 3951, 4236, 4417, 4718, 4909, 5226, 5553, 5760, 6103, 6320, 6679, 7048, 7281, 7666, 8061, 8310

Offset: 1

Author

Paolo Xausa, Mar 20 2024

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Main diagonal of A295573.

Cf. A000201, A001622, A101332, A101863, A101867, A371381.

Programs

Mathematica

Array[#^2 + Block[{q = Floor[# * GoldenRatio]}, q * (q + 1)] &, 100]

Python

from math import isqrt
def A371382(n): return n**2+(q:=n+isqrt(5*n**2)>>1)*(q+1) # Chai Wah Wu, Mar 21 2024