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