A066999 a(n) = 3^n * Sum_{i=1..n} i^3/3^i.

1, 11, 60, 244, 857, 2787, 8704, 26624, 80601, 242803, 729740, 2190948, 6575041, 19727867, 59186976, 177565024, 532699985, 1598105787, 4794324220, 14382980660, 43148951241, 129446864371, 388340605280, 1165021829664

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..200

Formula

Conjecture: g.f.:(-1-x^2-4*x)/((3*x-1)*(x-1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

a(n) = (11*3^(n+1) - 4*n^3 - 18*n^2 - 36*n - 33)/8. - Vaclav Kotesovec, Nov 28 2012

From Peter Bala, Nov 29 2012: (Start)

Recurrence equation: a(n) = 3*a(n-1) + n^3.

O.g.f.: x*(1 + 4*x + x^2)/((1 - 3*x)*(1 - x)^4) = x + 11*x^2 + 244*x^3 + .... See A047520 and A067534. (End)

Mathematica

f[n_] := 3^n*Sum[i^3/3^i, {i, n}]; Array[f, 24] (* Robert G. Wilson v, Nov 28 2012 *)

Prog

(PARI) { s=0; for (n=1, 200, s+=n^3/3^n; write("b066999.txt", n, " ", 3^n*s) ) } \\ Harry J. Smith, Apr 25 2010

Crossrefs

Cf. A008292, A047520, A067534.

Sequence in context: A044149 A044530 A050483 * A224291 A055826 A324622

Adjacent sequences: A066996 A066997 A066998 * A067000 A067001 A067002

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 27 2002

Status

approved