A359329 Number of diagonals in a regular polygon with n sides not passing through the center.

0, 0, 5, 6, 14, 16, 27, 30, 44, 48, 65, 70, 90, 96, 119, 126, 152, 160, 189, 198, 230, 240, 275, 286, 324, 336, 377, 390, 434, 448, 495, 510, 560, 576, 629, 646, 702, 720, 779, 798, 860, 880, 945, 966, 1034, 1056, 1127, 1150, 1224, 1248, 1325, 1350, 1430, 1456, 1539, 1566, 1652, 1680

Offset: 3

Author

Luk De Clercq, Dec 26 2022

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 3..10000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

A014106 and A054000 interleaved.

Cf. A000096, A142150.

Programs

Mathematica

Table[(n*(n - 4 + BitGet[n, 0]))/2, {n, 3, 100}] (* Paolo Xausa, Oct 02 2024 *)

Python

def A359329(n): return (n*(n-4)+n*(n&1))>>1 # Chai Wah Wu, Jan 23 2023

Formula

If n is odd, a(n) = (n^2 - 3*n)/2; if n is even, a(n) = (n^2 - 4*n)/2.

a(n) = A000096(n-3) - A142150(n-3).

G.f.: x^5*(5 + x - 2*x^2)/((1 - x)^3*(1 + x)^2). - Stefano Spezia, Jan 04 2023