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%I #44 Jan 16 2023 08:19:14
%S 0,1,7,15,28,43,63,85,112,141,175,211,252,295,343,393,448,505,567,631,
%T 700,771,847,925,1008,1093,1183,1275,1372,1471,1575,1681,1792,1905,
%U 2023,2143,2268,2395,2527,2661,2800,2941,3087,3235,3388,3543
%N Concentric heptagonal numbers.
%C A033582 and A069127 interleaved.
%C Partial sums of A047336. - _Reinhard Zumkeller_, Jan 07 2012
%H Vincenzo Librandi, <a href="/A195041/b195041.txt">Table of n, a(n) for n = 0..10000</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) = 7*n^2/4 + 3*((-1)^n - 1)/8.
%F From _R. J. Mathar_, Sep 28 2011: (Start)
%F G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x-1)^3 ).
%F a(n) + a(n+1) = A069099(n+1). (End)
%F a(n) = n^2 + floor(3*n^2/4). - _Bruno Berselli_, Aug 08 2013
%F Sum_{n>=1} 1/a(n) = Pi^2/42 + tan(sqrt(3/7)*Pi/2)*Pi/sqrt(21). - _Amiram Eldar_, Jan 16 2023
%t CoefficientList[Series[-((x (1+5 x+x^2))/((-1+x)^3 (1+x))),{x,0,80}],x] (* or *) LinearRecurrence[{2,0,-2,1},{0,1,7,15},80] (* _Harvey P. Dale_, Jan 18 2021 *)
%o (Magma) [7*n^2/4+3*((-1)^n-1)/8: n in [0..50]]; // _Vincenzo Librandi_, Sep 29 2011
%o (Haskell)
%o a195041 n = a195041_list !! n
%o a195041_list = scanl (+) 0 a047336_list
%o -- _Reinhard Zumkeller_, Jan 07 2012
%o (PARI) a(n)=7*n^2\4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Column 7 of A195040.
%Y Cf. A032527, A032528, A033582, A047336, A069099, A069127, A077221, A195042.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 27 2011
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