A174296 - OEIS

%I #11 Sep 08 2022 08:45:51

%S 1,2,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,

%T 2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,

%U 2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2

%N Row sums of A174294.

%H G. C. Greubel, <a href="/A174296/b174296.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).

%F a(A004280(n)) = 3 for n > 2.

%F From _G. C. Greubel_, Nov 25 2021: (Start)

%F a(n) = a(n-2) for n > 3, with a(0) = 1, a(1) = 2, a(2) = 2, a(3) = 3.

%F a(n) = (5 - (-1)^n)/2 for n > 1, with a(0) = 1, a(1) = 2.

%F a(n) = (n+1)*[n<2] + A010693(n)*[n>1].

%F G.f.: (1_+ 2*x + x^2 + x^3)/(1 - x^2).

%F E.g.f.: (1/2)*( -exp(-x) - 2*(1+x) + 5*exp(x) ). (End)

%t Table[If[n<2, n+1, (5-(-1)^n)/2], {n,0,110}] (* _G. C. Greubel_, Nov 25 2021 *)

%o (Magma) [n lt 2 select (n+1) else 2 + (n mod 2): n in [0..110]]; // _G. C. Greubel_, Nov 25 2021

%o (Sage) [1,2]+[(5-(-1)^n)/2 for n in (2..110)] # _G. C. Greubel_, Nov 25 2021

%Y Cf. A010693, A112468, A112467, A174294, A174295, A174297.

%K nonn,easy

%O 0,2

%A _Mats Granvik_, Mar 15 2010