A181509 a(1) = 2, a(n) = (n-th-even n^3) - (sum of previous terms)

2, 6, 56, 152, 296, 488, 728, 1016, 1352, 1736, 2168, 2648, 3176, 3752, 4376, 5048, 5768, 6536, 7352, 8216, 9128, 10088, 11096, 12152, 13256, 14408, 15608, 16856, 18152, 19496, 20888, 22328, 23816, 25352, 26936, 28568, 30248, 31976, 33752

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

a(n) = 56-72*n+24*n^2, n>2. a(n) = (2*n-2)^3-sum_{i=1..n-1} a(i). [From R. J. Mathar, Nov 01 2010]

For n>2, a(1)=56, a(2)=152, a(3)=296, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, May 05 2011]

G.f.: 2*x*(22*x^2+x^4+1)/(1-x)^3. - R. J. Mathar, Aug 26 2011

a(n)=8*A003215(n-2) for n>2. - J. M. Bergot, Aug 21 2013

Mathematica

Join[{2, 6}, Table[56-72n+24n^2, {n, 3, 42}]] (* or *) Join[{2, 6}, LinearRecurrence[{3, -3, 1}, {56, 152, 296}, 40]] (* Harvey P. Dale, May 05 2011 *)

Crossrefs

Cf. A000578.

Sequence in context: A084123 A193473 A336899 * A213026 A074023 A354315

Adjacent sequences: A181506 A181507 A181508 * A181510 A181511 A181512

Keyword

easy,nonn

Author

Giovanni Teofilatto, Oct 25 2010

Extensions

Corrected (replaced 2 and 4 by a 6 = 8-2) by R. J. Mathar, Nov 01 2010

Status

approved