A121512 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=1, a(2)=4, a(3)=10, a(4)=4.

1, 4, 10, 4, 7, 13, 7, 10, 16, 10, 13, 19, 13, 16, 22, 16, 19, 25, 19, 22, 28, 22, 25, 31, 25, 28, 34, 28, 31, 37, 31, 34, 40, 34, 37, 43, 37, 40, 46, 40, 43, 49, 43, 46, 52, 46, 49, 55, 49, 52, 58, 52, 55, 61, 55, 58, 64, 58, 61, 67, 61, 64, 70, 64, 67, 73

Offset: 1

Author

Roger L. Bagula, Sep 07 2006

Keywords

• nonn
• easy

Comments

This sequence gives a linearly increasing triangle shaped form on plotting.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A005448, A130806.

Programs

Mathematica

M = {{0, 1, 0}, {0, 0, 1}, {1, 0, 0}} v[1] = {1, 4, 10} v[n_] := v[n] = M.v[n - 1] + {0, 0, 3} a = Table[v[n][[1]], {n, 1, 50}]

Formula

G.f.: -x*(-1-3*x-6*x^2+7*x^3)/((1+x+x^2)*(x-1)^2). [Oct 14 2009]

a(n) = n+3 + (-1)^n * A130806(n+1). [Oct 14 2009]

a(n) = (24*n + 75 - 18*cos(2*(n+1)*Pi/3) + 9*cos(2*Pi*sin(2*n*Pi/3)/sqrt(3)) + 50*sqrt(3)*sin(2*(n+1)*Pi/3))/24. - Wesley Ivan Hurt, Oct 05 2017

Extensions

Definition replaced by recurrence - The Assoc. Editors of the OEIS, Oct 14 2009