A213039 a(n) = n^3 - floor(n/3)^3.

0, 1, 8, 26, 63, 124, 208, 335, 504, 702, 973, 1304, 1664, 2133, 2680, 3250, 3971, 4788, 5616, 6643, 7784, 8918, 10305, 11824, 13312, 15113, 17064, 18954, 21223, 23660, 26000, 28791, 31768, 34606, 37973, 41544, 44928, 48925, 53144, 57122

Offset

0,3

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).

Formula

a(n) = a(n-1)+3*a(n-3)-3*a(n-4)-3*a(n-6)+3*a(n-7)+a(n-9)-a(n-10).

G.f.: (x^2 + 7*x^3 + 18*x^4 + 34*x^5 + 40*x^6 + 30*x^7 + 19*x^8 + 7*x^9)/(1 - x - 3*x^3 + 3*x^4 + 3*x^6 - 3*x^7 - x^9 + x^10).

Mathematica

a[n_] := n^3 - Floor[n/3]^3
Table[a[n], {n, 0, 90}]    (* A213039 *)
LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {0, 1, 8, 26, 63, 124, 208, 335, 504, 702}, 90]

Crossrefs

Sequence in context: A252870 A163121 A250352 * A211640 A002901 A350163

Adjacent sequences: A213036 A213037 A213038 * A213040 A213041 A213042

Keyword

nonn,easy

Author

Clark Kimberling, Jun 06 2012

Status

approved