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

3,3

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).

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

Mathematica

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

Prog

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

Crossrefs

A014106 and A054000 interleaved.

Cf. A000096, A142150.

Sequence in context: A289895 A335785 A266304 * A308839 A099330 A322479

Adjacent sequences: A359326 A359327 A359328 * A359330 A359331 A359332

Keyword

nonn,easy

Author

Luk De Clercq, Dec 26 2022

Status

approved