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A195049
Concentric 21-gonal numbers.
7
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
0,3
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
MAPLE
A195049:=n->21*n^2/4+17*((-1)^n-1)/8: seq(A195049(n), n=0..100); # Wesley Ivan Hurt, Jan 17 2017
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {0, 1, 21, 43}, 50] (* Amiram Eldar, Jan 17 2023 *)
PROG
(PARI) a(n)=21*n^2/4+17*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Column 21 of A195040.
Sequence in context: A041868 A135391 A118569 * A041874 A041872 A041876
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 27 2011
STATUS
approved