A371388 a(n) = 2*n*floor(n*(1 + sqrt(5))/2) - n^2. Main diagonal of A340429.

1, 8, 15, 32, 55, 72, 105, 128, 171, 220, 253, 312, 377, 420, 495, 544, 629, 720, 779, 880, 945, 1056, 1173, 1248, 1375, 1508, 1593, 1736, 1827, 1980, 2139, 2240, 2409, 2584, 2695, 2880, 2997, 3192, 3393, 3520, 3731, 3864, 4085, 4312, 4455, 4692, 4935, 5088, 5341

Offset

1,2

Links

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

Formula

a(n) = 2*n*A000201(n) - n^2.

Mathematica

Array[2 * # * Floor[# * GoldenRatio] - #^2 &, 100]

Prog

(Python)
from math import isqrt
def A371388(n): return n*((n+isqrt(5*n**2)&-2)-n) # Chai Wah Wu, Mar 21 2024

Crossrefs

Cf. A340429.

Cf. A000201, A001622.

Sequence in context: A123526 A083686 A293360 * A287644 A089954 A134020

Adjacent sequences: A371385 A371386 A371387 * A371389 A371390 A371391

Keyword

nonn,easy

Author

Paolo Xausa, Mar 21 2024

Status

approved