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A195047 Concentric 17-gonal numbers. 7

%I #33 Jan 16 2023 08:19:58

%S 0,1,17,35,68,103,153,205,272,341,425,511,612,715,833,953,1088,1225,

%T 1377,1531,1700,1871,2057,2245,2448,2653,2873,3095,3332,3571,3825,

%U 4081,4352,4625,4913,5203,5508,5815,6137,6461,6800,7141,7497,7855,8228,8603,8993

%N Concentric 17-gonal numbers.

%C Also concentric heptadecagonal numbers or concentric heptakaidecagonal numbers.

%H Ivan Panchenko, <a href="/A195047/b195047.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F a(n) = 17*n^2/4+13*((-1)^n-1)/8. [Typo fixed by _Ivan Panchenko_, Nov 08 2013]

%F From _R. J. Mathar_, Sep 28 2011: (Start)

%F G.f.: -x*(1+15*x+x^2) / ( (1+x)*(x-1)^3 ).

%F a(n)+a(n+1) = A069130(n+1). (End)

%F From _Bruno Berselli_, Sep 29 2011: (Start)

%F a(n) = a(-n) = (34*n^2+13*(-1)^n-13)/8.

%F a(n) = A151978(A061925(n)). (End)

%F Sum_{n>=1} 1/a(n) = Pi^2/102 + tan(sqrt(13/17)*Pi/2)*Pi/sqrt(221). - _Amiram Eldar_, Jan 16 2023

%t LinearRecurrence[{2,0,-2,1},{0,1,17,35},50] (* _Harvey P. Dale_, Dec 23 2017 *)

%o (PARI) a(n)=17*n^2/4+13*((-1)^n-1)/8 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Column 17 of A195040.

%Y Cf. A032527, A032528, A061925, A069130, A151978, A195046, A195048, A195146, A195147.

%K nonn,easy

%O 0,3

%A _Omar E. Pol_, Sep 27 2011

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)