A211786 n^3 + floor(n^3/2).

1, 12, 40, 96, 187, 324, 514, 768, 1093, 1500, 1996, 2592, 3295, 4116, 5062, 6144, 7369, 8748, 10288, 12000, 13891, 15972, 18250, 20736, 23437, 26364, 29524, 32928, 36583, 40500, 44686, 49152, 53905, 58956, 64312, 69984, 75979, 82308

Offset

1,2

Comments

Row 2 of the array A211785.

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).

Formula

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

G.f.: x*(1+9*x+6*x^2+2*x^3)/((1+x)*(1-x)^4). [Bruno Berselli, May 06 2012]

a(n) = floor(3*n^3/2) = (6*n^3+(-1)^n-1)/4. [Bruno Berselli, May 06 2012]

Mathematica

f[n_, m_] := Sum[Floor[n^3/k], {k, 1, m}]
t = Table[f[n, 2], {n, 1, 90}]
FindLinearRecurrence[t]
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 12, 40, 96, 187}, 38] (* Ray Chandler, Aug 02 2015 *)

Prog

(Magma) [n^3+Floor(n^3/2): n in [1..38]]; // Bruno Berselli, May 06 2012

Crossrefs

Cf. A032766 (n+floor(n/2)), A032528 (n^2+floor(n^2/2)), A211701.

Sequence in context: A109766 A365446 A033586 * A320252 A350124 A359566

Adjacent sequences: A211783 A211784 A211785 * A211787 A211788 A211789

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2012

Status

approved