cp's OEIS Frontend

A354595 a(n) = n^2 + 4*floor(n/2)^2.

%I A354595 #19 Jul 08 2022 08:23:54
%S A354595 0,1,8,13,32,41,72,85,128,145,200,221,288,313,392,421,512,545,648,685,
%T A354595 800,841,968,1013,1152,1201,1352,1405,1568,1625,1800,1861,2048,2113,
%U A354595 2312,2381,2592,2665,2888,2965,3200,3281,3528,3613,3872
%N A354595 a(n) = n^2 + 4*floor(n/2)^2.
%C A354595 The first bisection is A139098, the second bisection is A102083.
%H A354595 David Lovler, <a href="/A354595/b354595.txt">Table of n, a(n) for n = 0..10000</a>
%H A354595 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A354595 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), n >= 5.
%F A354595 a(n) = A000290(n) + 4*A008794(n).
%F A354595 G.f.: x*(1 + 7*x + 3*x^2 + 5*x^3)/((1 - x)^3*(1 + x)^2).
%F A354595 E.g.f.: 2*x^2*cosh(x) + (1 + 2*x + 2*x^2)*sinh(x). - _Stefano Spezia_, Jun 07 2022
%t A354595 a[n_] := n^2 + 4 Floor[n/2]^2
%t A354595 Table[a[n], {n, 0, 90}]    (* A354595 *)
%t A354595 LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 8, 13, 32}, 60]
%o A354595 (PARI) a(n) = n^2 + 4*(n\2)^2;
%Y A354595 Cf. A000290, A008794, A102083, A139098, A247375.
%Y A354595 Cf. A213037, A327259 (diagonal), A354594, A354596.
%K A354595 nonn,easy
%O A354595 0,3
%A A354595 _David Lovler_, Jun 01 2022