A174296 Row sums of A174294.

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, 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, 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

Offset: 0

Author

Mats Granvik, Mar 15 2010

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

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

Programs

Magma

[n lt 2 select (n+1) else 2 + (n mod 2): n in [0..110]]; // G. C. Greubel, Nov 25 2021

Mathematica

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

Sage

[1,2]+[(5-(-1)^n)/2 for n in (2..110)] # G. C. Greubel, Nov 25 2021

Formula

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

From G. C. Greubel, Nov 25 2021: (Start)

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

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

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

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

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