A213030 a(n) = floor(2*n/3)^2 - floor(n/3)^2.

0, 0, 1, 3, 3, 8, 12, 12, 21, 27, 27, 40, 48, 48, 65, 75, 75, 96, 108, 108, 133, 147, 147, 176, 192, 192, 225, 243, 243, 280, 300, 300, 341, 363, 363, 408, 432, 432, 481, 507, 507, 560, 588, 588, 645, 675, 675, 736, 768, 768, 833, 867, 867, 936, 972

Offset

0,4

Links

Table of n, a(n) for n=0..54.

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

Formula

a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7).

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

Mathematica

a[n_] := Floor[2*n/3]^2 - Floor[n/3]^2
Table[a[n], {n, 0, 60}]    (* A213030 *)
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {0, 0, 1, 3, 3, 8, 12}, 60] (* Harvey P. Dale, Jul 06 2021 *)

Crossrefs

Sequence in context: A358834 A346005 A276552 * A364468 A303902 A090597

Adjacent sequences: A213027 A213028 A213029 * A213031 A213032 A213033

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2012

Status

approved