A346004 If n even then n otherwise ((n+1)/2)^2.

0, 1, 2, 4, 4, 9, 6, 16, 8, 25, 10, 36, 12, 49, 14, 64, 16, 81, 18, 100, 20, 121, 22, 144, 24, 169, 26, 196, 28, 225, 30, 256, 32, 289, 34, 324, 36, 361, 38, 400, 40, 441, 42, 484, 44, 529, 46, 576, 48, 625, 50, 676, 52, 729, 54, 784, 56, 841, 58, 900, 60, 961, 62, 1024, 64, 1089

Offset: 0

Author

N. J. A. Sloane, Jul 25 2021

Keywords

• nonn
• easy

References

• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. Sequence can be seen in the circled numbers at foot of page 63.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A125714, A346005-A346007, A346595.

Programs

Mathematica

A346004[n_] := If[OddQ[n], (n+1)^2/4, n]; Array[A346004, 100, 0] (* or *)
Riffle[#-2, #^2/4] & [Range[2, 100, 2]] (* Paolo Xausa, Aug 28 2024 *)

Python

def A346004(n): return ((n+1)//2)**2 if n % 2 else n # Chai Wah Wu, Jul 25 2021

Formula

G.f.: x*(-1-2*x-x^2+2*x^3) / ( (x-1)^3*(1+x)^3 ). - R. J. Mathar, Aug 05 2021

a(n) = ((n^2 + 6*n + 1) - (n-1)^2*(-1)^n)/8. - Aaron J Grech, Aug 27 2024