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A354594 a(n) = n^2 + 2*floor(n/2)^2.

%I A354594 #19 Jul 08 2022 08:23:46
%S A354594 0,1,6,11,24,33,54,67,96,113,150,171,216,241,294,323,384,417,486,523,
%T A354594 600,641,726,771,864,913,1014,1067,1176,1233,1350,1411,1536,1601,1734,
%U A354594 1803,1944,2017,2166,2243,2400,2481,2646,2731,2904
%N A354594 a(n) = n^2 + 2*floor(n/2)^2.
%C A354594 The first bisection is A033581, the second bisection is A080859. - _Bernard Schott_, Jun 07 2022
%H A354594 David Lovler, <a href="/A354594/b354594.txt">Table of n, a(n) for n = 0..10000</a>
%H A354594 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A354594 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), n >= 5.
%F A354594 a(n) = A000290(n) + 2*A008794(n).
%F A354594 G.f.: x*(1 + 5*x + 3*x^2 + 3*x^3)/((1 - x)^3*(1 + x)^2).
%F A354594 E.g.f.: (x*(1 + 3*x)*cosh(x) + (1 + 3*x + 3*x^2)*sinh(x))/2. - _Stefano Spezia_, Jun 07 2022
%t A354594 a[n_] := n^2 + 2 Floor[n/2]^2
%t A354594 Table[a[n], {n, 0, 90}]    (* A354594 *)
%t A354594 LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 6, 11, 24}, 60]
%o A354594 (PARI) a(n) = n^2 + 2*(n\2)^2;
%Y A354594 Cf. A000290, A008794, A033581, A080859, A247375.
%Y A354594 Cf. A213037, A322744 (diagonal), A354595, A354596.
%K A354594 nonn,easy
%O A354594 0,3
%A A354594 _David Lovler_, Jun 01 2022