A147691 G.f.: x*(1+x+x^2)*(1+6*x+8*x^2+4*x^3-x^4)/((1+x)^2*(1-x)^4).

0, 1, 9, 34, 91, 192, 353, 584, 903, 1318, 1849, 2502, 3299, 4244, 5361, 6652, 8143, 9834, 11753, 13898, 16299, 18952, 21889, 25104, 28631, 32462, 36633, 41134, 46003, 51228, 56849, 62852, 69279, 76114, 83401, 91122, 99323, 107984, 117153, 126808

Offset

0,3

Comments

The inverse Motzkin transform of A057586, which means that the substitution x -> x*A001006(x) for the independent variable in the g.f. yields the g.f. of A057586.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6), n> 7.

a(n) = (3*n*(6*n^2-12*n+13)+(n-2)*(-1)^n-6)/8 for n>1, a(0)=0, a(1)=1. [Bruno Berselli, Dec 11 2012]

Mathematica

CoefficientList[Series[x (1 + x + x^2) (1 + 6 x + 8 x^2 + 4 x^3 - x^4)/((1 + x)^2 (1 - x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 11 2012 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 9, 34, 91, 192, 353, 584}, 40] (* Harvey P. Dale, Jun 23 2017 *)

Prog

(Magma) I:=[0, 1, 9, 34, 91, 192, 353, 584]; [n le 8 select I[n] else 2*Self(n-1)+Self(n-2)-4*Self(n-3)+Self(n-4)+2*Self(n-5)-Self(n-6): n in [1..40]]; // Vincenzo Librandi, Dec 11 2012

Crossrefs

Sequence in context: A293038 A326278 A014816 * A000441 A067989 A002881

Adjacent sequences: A147688 A147689 A147690 * A147692 A147693 A147694

Keyword

nonn,easy

Author

R. J. Mathar, Nov 10 2008

Status

approved