A173961 Averages of two consecutive even cubes: (n^3+(n+2)^3)/2.

4, 36, 140, 364, 756, 1364, 2236, 3420, 4964, 6916, 9324, 12236, 15700, 19764, 24476, 29884, 36036, 42980, 50764, 59436, 69044, 79636, 91260, 103964, 117796, 132804, 149036, 166540, 185364, 205556, 227164, 250236, 274820, 300964, 328716, 358124

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(4+20*x+20*x^2+4*x^3)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 04 2012

a(n) = 8n^3 - 12n^2 + 12n - 4. - Charles R Greathouse IV, Jan 02 2012

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jul 02 2012

a(n) = 4 * A005898(n-1).

Example

(0^3+2^3)/2=4, (2^3+4^3)/2=36, ....

Mathematica

f[n_]:=(n^3+(n+2)^3)/2; Table[f[n], {n, 0, 5!, 2}]
CoefficientList[Series[(4+20*x+20*x^2+4*x^3)/(1-4*x+6*x^2-4*x^3+x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 02 2012 *)

Prog

(PARI) a(n)=4*n*(2*n^2-3*n+3)-4 \\ Charles R Greathouse IV, Jan 02 2012
(Magma) I:=[4, 36, 140, 364]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 02 2012

Crossrefs

Cf. A005898, A027575, A173960.

Sequence in context: A060783 A296948 A125756 * A340661 A035287 A183354

Adjacent sequences: A173958 A173959 A173960 * A173962 A173963 A173964

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 03 2010

Status

approved