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A190716 a(2*n) = 2*n and a(2*n-1) = A054569(n).

%I A190716 #11 Aug 19 2025 08:53:36
%S A190716 1,2,7,4,21,6,43,8,73,10,111,12,157,14,211,16,273,18,343,20,421,22,
%T A190716 507,24,601,26,703,28,813,30,931,32,1057,34,1191,36,1333,38,1483,40,
%U A190716 1641,42,1807,44,1981,46,2163,48,2353,50,2551,52,2757,54,2971,56,3193
%N A190716 a(2*n) = 2*n and a(2*n-1) = A054569(n).
%C A190716 Equals the Row2 triangle sums of the Connell sequence A001614 as a triangle. The Row2(n) triangle sums are defined by Row2(n) = sum((-1)^(n+k)*T(n,k), k=1..n), see A180662.
%H A190716 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A190716 a(2*n) = 2*n and a(2*n-1) = 4*n^2 - 6*n + 3.
%F A190716 G.f.: x*(1+2*x+4*x^2-2*x^3+3*x^4)/(1-x^2)^3.
%F A190716 From _Stefano Spezia_, Aug 19 2025: (Start)
%F A190716 a(n) = (1 - (-1)^n*(n - 1)^2 + n^2)/2.
%F A190716 E.g.f.: (1 + x + x^2)*sinh(x). (End)
%p A190716 A190716:= n-> coeff (series (x*(1+2*x+4*x^2-2*x^3+3*x^4)/(1-x^2)^3, x, n+1), x, n): seq(A190716(n), n=1..49);
%t A190716 a[n_]:=(1-(-1)^n(n-1)^2+n^2)/2; Array[a,57] (* _Stefano Spezia_, Aug 19 2025 *)
%Y A190716 Cf. A001614, A054569, A180662.
%K A190716 nonn,easy
%O A190716 1,2
%A A190716 _Johannes W. Meijer_, May 18 2011