A140144 a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^0 if n is even.

1, 2, 5, 6, 11, 12, 19, 20, 29, 30, 41, 42, 55, 56, 71, 72, 89, 90, 109, 110, 131, 132, 155, 156, 181, 182, 209, 210, 239, 240, 271, 272, 305, 306, 341, 342, 379, 380, 419, 420, 461, 462, 505, 506, 551, 552, 599, 600, 649, 650, 701, 702, 755, 756, 811, 812, 869

Offset: 1

Author

Artur Jasinski, May 12 2008

Keywords

• nonn
• easy

Comments

Equals triangle A177990 * [1,2,3,...]. - Gary W. Adamson, May 16 2010

Links

• Girtrude Hamm, Classification of lattice triangles by their two smallest widths, arXiv:2304.03007 [math.CO], 2023.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.

Cf. A177990. - Gary W. Adamson, May 16 2010

Cf. A002378 (even bisection), A028387 (odd bisection).

Programs

Mathematica

a = {}; r = 1; s = 0; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a

Formula

From R. J. Mathar, Feb 22 2009: (Start)

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).

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

a(n) = Sum_{k=1..n} k^(k mod 2). - Wesley Ivan Hurt, Nov 20 2021