A195049 Concentric 21-gonal numbers.
0, 1, 21, 43, 84, 127, 189, 253, 336, 421, 525, 631, 756, 883, 1029, 1177, 1344, 1513, 1701, 1891, 2100, 2311, 2541, 2773, 3024, 3277, 3549, 3823, 4116, 4411, 4725, 5041, 5376, 5713, 6069, 6427, 6804, 7183, 7581, 7981, 8400, 8821, 9261, 9703, 10164
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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Maple
A195049:=n->21*n^2/4+17*((-1)^n-1)/8: seq(A195049(n), n=0..100); # Wesley Ivan Hurt, Jan 17 2017
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Mathematica
LinearRecurrence[{2, 0, -2, 1}, {0, 1, 21, 43}, 50] (* Amiram Eldar, Jan 17 2023 *) -
PARI
a(n)=21*n^2/4+17*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 21*n^2/4 + 17*((-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+19*x+x^2)/((1-x)^3*(1+x)). (End)
Sum_{n>=1} 1/a(n) = Pi^2/126 + tan(sqrt(17/21)*Pi/2)*Pi/sqrt(357). - Amiram Eldar, Jan 17 2023