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A167149 10000-gonal numbers: a(n) = n + 4999 * n * (n-1).

%I A167149 #34 Sep 30 2017 23:48:01
%S A167149 0,1,10000,29997,59992,99985,149976,209965,279952,359937,449920,
%T A167149 549901,659880,779857,909832,1049805,1199776,1359745,1529712,1709677,
%U A167149 1899640,2099601,2309560,2529517,2759472,2999425,3249376,3509325,3779272,4059217,4349160,4649101
%N A167149 10000-gonal numbers: a(n) = n + 4999 * n * (n-1).
%C A167149 There are infinitely many 10000-gonal numbers that are also squares. The first seven are at n = 0, 1, 2, 21, 9800, 173774514938177, 1042188013912456. - _Muniru A Asiru_, Apr 10 2016
%H A167149 G. C. Greubel, <a href="/A167149/b167149.txt">Table of n, a(n) for n = 0..1000</a>
%H A167149 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A167149 From _R. J. Mathar_, Nov 02 2009: (Start)
%F A167149 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A167149 G.f.: x*(1 + 9997*x)/(1-x)^3. (End)
%F A167149 E.g.f.: exp(x)*x*(1 + 4999*x). - _Ilya Gutkovskiy_, Apr 10 2016
%p A167149 P := proc(n,k) n*((k-2)*n-k+4)/2 ; end: A167149 := proc(n) P(n,10000) ; end: seq(A167149(n),n=0..50) ; # _R. J. Mathar_, Nov 02 2009
%t A167149 Table[n + 4999 n (n - 1), {n, 0, 31}] (* or *)
%t A167149 CoefficientList[Series[x (1 + 9997 x)/(1 - x)^3, {x, 0, 31}], x] (* _Michael De Vlieger_, Apr 10 2016 *)
%t A167149 LinearRecurrence[{3, -3, 1}, {0, 1, 10000}, 10] (* _G. C. Greubel_, Jun 04 2016 *)
%o A167149 (PARI) x='x+O('x^99); concat(0, Vec(x*(1+9997*x)/(1-x)^3)) \\ _Altug Alkan_, Apr 10 2016
%o A167149 (GAP)
%o A167149 A167149:=List([1..10^2],n->n+499*n*(n-1)); # _Muniru A Asiru_, Sep 27 2017
%Y A167149 Cf. A057145. - _R. J. Mathar_, Nov 02 2009
%K A167149 nonn,easy
%O A167149 0,3
%A A167149 Michael G. Fenner (sidk.20c(AT)gmail.com), Oct 28 2009
%E A167149 Edited (but not checked) by _N. J. A. Sloane_, Nov 01 2009
%E A167149 Sequence extended by _R. J. Mathar_, Nov 02 2009