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%I #44 Feb 27 2022 05:46:50
%S 0,10,52,126,232,370,540,742,976,1242,1540,1870,2232,2626,3052,3510,
%T 4000,4522,5076,5662,6280,6930,7612,8326,9072,9850,10660,11502,12376,
%U 13282,14220,15190,16192,17226,18292,19390,20520,21682,22876,24102,25360,26650,27972
%N Even 10-gonal (or decagonal) numbers.
%C a(n) (for n >= 1) is also the Wiener index of the windmill graph D(5, n). The windmill graph D(m, n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e. a bouquet of n pieces of K_m graphs). The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph. The Wiener index of D(m, n) is (1/2)n(m-1)[(m-1)(2n-1)+1]. For the Wiener indices of D(3, n), D(4, n), and D(6, n) see A033991, A152743, and A180577, respectively. - _Emeric Deutsch_, Sep 21 2010
%H Vincenzo Librandi, <a href="/A028994/b028994.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DecagonalNumber.html">Decagonal Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WindmillGraph.html">Windmill Graph</a>. - _Emeric Deutsch_, Sep 21 2010
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 2*n*(8*n - 3). - _Omar E. Pol_, Aug 19 2011
%F G.f.: -2*x*(11*x+5)/(x-1)^3. - _Colin Barker_, Nov 18 2012
%F Sum_{n>=1} 1/a(n) = (8*log(2) - (sqrt(2)-1)*Pi - 2*sqrt(2)*log(1+sqrt(2)))/12. - _Amiram Eldar_, Feb 27 2022
%t CoefficientList[Series[-2 x (11 x + 5)/(x - 1)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 18 2013 *)
%t LinearRecurrence[{3, -3, 1}, {0, 10, 52}, 40] (* _Harvey P. Dale_, Dec 10 2014 *)
%t Table[16n^2 - 6n, {n, 0, 49}] (* _Alonso del Arte_, Jan 24 2017 *)
%o (Magma) [2*n*(8*n - 3): n in [0..60]]; // _Vincenzo Librandi_, Oct 18 2013
%o (PARI) a(n)=2*n*(8*n-3) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A033991, A152743, A180577, A001107, A028993, A139273.
%K nonn,easy
%O 0,2
%A _Patrick De Geest_
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