A195058 Concentric 23-gonal numbers.
0, 1, 23, 47, 92, 139, 207, 277, 368, 461, 575, 691, 828, 967, 1127, 1289, 1472, 1657, 1863, 2071, 2300, 2531, 2783, 3037, 3312, 3589, 3887, 4187, 4508, 4831, 5175, 5521, 5888, 6257, 6647, 7039, 7452, 7867, 8303, 8741, 9200, 9661, 10143, 10627
Offset: 0
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
Programs
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Mathematica
Table[23n^2/4 + 19((-1)^n - 1)/8, {n, 0, 49}] (* Alonso del Arte, Jan 23 2015 *) LinearRecurrence[{2,0,-2,1},{0,1,23,47},50] (* Harvey P. Dale, Jul 22 2023 *) -
PARI
a(n)=23*n^2/4+19*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 23*n^2/4 + 19*((-1)^n-1)/8.
From Colin Barker, Sep 16 2012: (Start)
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: x*(1 + 21*x + x^2)/((1-x)^3*(1+x)). (End)
Sum_{n>=1} 1/a(n) = Pi^2/138 + tan(sqrt(19/23)*Pi/2)*Pi/sqrt(437). - Amiram Eldar, Jan 17 2023