A048840 Expansion of (1 - x + 2*x^2 + 2*x^3 - x^4 - x^5)/(1-x)^3.

1, 2, 5, 12, 22, 34, 48, 64, 82, 102, 124, 148, 174, 202, 232, 264, 298, 334, 372, 412, 454, 498, 544, 592, 642, 694, 748, 804, 862, 922, 984, 1048, 1114, 1182, 1252, 1324, 1398, 1474, 1552, 1632, 1714, 1798, 1884, 1972, 2062, 2154, 2248, 2344, 2442, 2542

Offset

0,2

Comments

Also, number of permutations of length n+1 which avoid the patterns 321, 1342, 2134. - Lara Pudwell, Feb 26 2006

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

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

Formula

For n > 2, a(n) = n^2 + 3n - 6.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5. - Colin Barker, May 03 2019

Mathematica

CoefficientList[Series[(1-x+2*x^2+2*x^3-x^4-x^5)/(1-x)^3, {x, 0, 60}], x] (* or *) Join[{1, 2, 5}, Table[n^2+3*n-6, {n, 3, 60}]] (* or *) Join[{1, 2, 5}, LinearRecurrence[{3, -3, 1}, {12, 22, 34}, 58]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)

Prog

(PARI) Vec((1-x+2*x^2+2*x^3-x^4-x^5)/(1-x)^3 + O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012, corrected by Colin Barker, May 03 2019

Crossrefs

Sequence in context: A368969 A116727 A116729 * A116718 A026035 A215183

Adjacent sequences: A048837 A048838 A048839 * A048841 A048842 A048843

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved