A213031 [n/2]^3 -[n/3]^3, where []=floor.

0, 0, 1, 0, 7, 7, 19, 19, 56, 37, 98, 98, 152, 152, 279, 218, 387, 387, 513, 513, 784, 657, 988, 988, 1216, 1216, 1685, 1468, 2015, 2015, 2375, 2375, 3096, 2765, 3582, 3582, 4104, 4104, 5131, 4662, 5803, 5803, 6517, 6517, 7904, 7273, 8792, 8792

Offset

0,5

Links

Table of n, a(n) for n=0..47.

Index entries for linear recurrences with constant coefficients, signature (-2,0,5,7,0,-9,-9,0,7,5,0,-2,-1).

Formula

a(n) = -2*a(n-1)+5*a(n-3)+7*a(n-4)-9*a(n-6)-9*a(n-7)+7*a(n-9)+5*a(n-10)-2*a(n-12)-a(n-12).

G.f.: (x^2 + 2*x^3 + 7*x^4 + 16*x^5 + 26*x^6 + 22*x^7 + 19*x^8 + 14*x^9 + 7*x^10)/(1 + 2*x - 5*x^3 - 7*x^4 + 9*x^6 + 9*x^7 - 7*x^9 - 5*x^10 + 2*x^12 + x^13).

Mathematica

a[n_] := Floor[n/2]^3 - Floor[n/3]^3
Table[a[n], {n, 0, 60}]  (* A213031 *)
LinearRecurrence[{-2, 0, 5, 7, 0, -9, -9, 0, 7, 5, 0, -2, -1}, {0, 0, 1, 0, 7, 7, 19, 19, 56, 37, 98, 98, 152}, 60]

Crossrefs

Sequence in context: A070847 A195863 A053416 * A299453 A300091 A094248

Adjacent sequences: A213028 A213029 A213030 * A213032 A213033 A213034

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2012

Status

approved