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%I #20 Jan 16 2023 08:20:19
%S 0,1,15,31,60,91,135,181,240,301,375,451,540,631,735,841,960,1081,
%T 1215,1351,1500,1651,1815,1981,2160,2341,2535,2731,2940,3151,3375,
%U 3601,3840,4081,4335,4591,4860,5131,5415,5701,6000,6301,6615,6931,7260,7591
%N Concentric 15-gonal numbers.
%H Harvey P. Dale, <a href="/A195046/b195046.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) = 15*n^2/4+11*((-1)^n-1)/8.
%F From _Harvey P. Dale_, Feb 23 2012: (Start)
%F a(0)=0, a(1)=1, a(2)=15, a(3)=31, a(n)=2*a(n-1)-2*a(n-3)+a(n-4).
%F G.f.: -((x*(1+x*(13+x)))/((-1+x)^3*(1+x))). (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/90 + tan(sqrt(11/15)*Pi/2)*Pi/sqrt(165). - _Amiram Eldar_, Jan 16 2023
%t Table[15n^2/4+11((-1)^n-1)/8,{n,0,50}] (* or *) LinearRecurrence[ {2,0,-2,1},{0,1,15,31},50] (* _Harvey P. Dale_, Feb 23 2012 *)
%o (PARI) a(n)=15*n^2/4+11*((-1)^n-1)/8 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Column 15 of A195040.
%Y Cf. A032527, A032528, A195045, A195047, A195145, A195146.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 27 2011
%E a(1)=1 added by _Harvey P. Dale_, Feb 23 2012
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