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%I #19 Apr 12 2023 08:27:51
%S 2,17,57,134,260,447,707,1052,1494,2045,2717,3522,4472,5579,6855,8312,
%T 9962,11817,13889,16190,18732,21527,24587,27924,31550,35477,39717,
%U 44282,49184,54435,60047,66032,72402,79169,86345,93942,101972,110447,119379
%N a(n) = n*(4*n^2 + n - 1)/2.
%C a(n) = Sum_{k=1..n} (4*n*k - n - k), sums of rows of the triangle in A125199.
%C A003415(A003415(a(n))) = 2*A016969(n-1).
%H Harvey P. Dale, <a href="/A125200/b125200.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _R. J. Mathar_, Feb 12 2010
%F G.f.: x*(2+9*x+x^2)/(x-1)^4. - _R. J. Mathar_, Feb 12 2010
%F a(n) = Sum_{i=1..n} A033568(i). - _Bruno Berselli_, Jul 22 2013
%t LinearRecurrence[{4,-6,4,-1},{2,17,57,134},40] (* _Harvey P. Dale_, Feb 05 2013 *)
%o (Magma) [n*(4*n^2 +n-1)div 2:n in [1..40]]; // _Vincenzo Librandi_, Dec 27 2010
%Y Cf. A003415, A016969, A033568, A125199.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, Nov 24 2006
%E Definition corrected by _Vincenzo Librandi_, Dec 27 2010
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