A036407 a(n) = ceiling(n^2/9).

0, 1, 1, 1, 2, 3, 4, 6, 8, 9, 12, 14, 16, 19, 22, 25, 29, 33, 36, 41, 45, 49, 54, 59, 64, 70, 76, 81, 88, 94, 100, 107, 114, 121, 129, 137, 144, 153, 161, 169, 178, 187, 196, 206, 216, 225, 236, 246, 256, 267, 278, 289, 301, 313, 324, 337, 349

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).

Programs

Magma

[Ceiling(n^2/9) : n in [0..100]]; // Wesley Ivan Hurt, Mar 10 2015

Maple

A036407:=n->ceil(n^2/9): seq(A036407(n), n=0..100); # Wesley Ivan Hurt, Mar 10 2015

Mathematica

Table[Ceiling[n^2/9], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 10 2015 *)
LinearRecurrence[{2,-1,0,0,0,0,0,0,1,-2,1},{0,1,1,1,2,3,4,6,8,9,12},60] (* Harvey P. Dale, Nov 02 2020 *)

Formula

From R. J. Mathar, Jan 22 2011: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11).

G.f.: -x*(1+x)*(x^8 - 2*x^7 + 2*x^6 - x^5 + x^4 - x^3 + 2*x^2 - 2*x + 1) / ( (1+x+x^2)*(x^6+x^3+1)*(x-1)^3 ). (End)