A089830 Expansion of (1-3*x+6*x^2-5*x^3+3*x^4-x^5)/(1-x)^6.

1, 3, 9, 24, 57, 122, 239, 435, 745, 1213, 1893, 2850, 4161, 5916, 8219, 11189, 14961, 19687, 25537, 32700, 41385, 51822, 64263, 78983, 96281, 116481, 139933, 167014, 198129, 233712, 274227, 320169, 372065, 430475, 495993, 569248, 650905, 741666, 842271

Offset

0,2

Links

Table of n, a(n) for n=0..38.

A. Burstein and T. Mansour, Words restricted by 3-letter ..., arXiv:math/0112281 [math.CO], 2001.

A. Burstein and T. Mansour, Words restricted by 3-letter ..., Annals. Combin., 7 (2003), 1-14; see Example 3.5.

S. Kitaev, J. Remmel, p-Ascent Sequences, arXiv preprint arXiv:1503.00914 [math.CO], 2015.

Sergey Kitaev, J. B. Remmel, A note on p-Ascent Sequences, Preprint, 2016.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(0)=1, a(1)=3, a(2)=9, a(3)=24, a(4)=57, a(5)=122, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). -Harvey P. Dale, Jul 18 2012

a(n) = 13*n/15+1+n^3/8+11*n^2/12+n^5/120+n^4/12. - R. J. Mathar, Sep 27 2014

Mathematica

CoefficientList[Series[(1-3x+6x^2-5x^3+3x^4-x^5)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 3, 9, 24, 57, 122}, 40] (* Harvey P. Dale, Jul 18 2012 *)

Prog

(Magma) I:=[1, 3, 9, 24, 57, 122]; [n le 6 select I[n] else 6*Self(n-1)- 15*Self(n-2)+ 20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Nov 19 2015

Crossrefs

Sequence in context: A085739 A245762 A291706 * A258111 A360197 A109175

Adjacent sequences: A089827 A089828 A089829 * A089831 A089832 A089833

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 18 2004

Status

approved