A219756 Expansion of x^4*(1-7*x+17*x^2-18*x^3+11*x^4-5*x^5)/((1-x)^2*(1-3*x)^2*(1-3*x+x^2)^2).

0, 0, 0, 0, 1, 7, 34, 141, 537, 1942, 6786, 23143, 77513, 256021, 836330, 2707652, 8701723, 27793375, 88310920, 279354069, 880300371, 2764788010, 8658249900, 27045078415, 84287831231, 262161737197, 813944768564, 2523027912296, 7809442203157, 24140652097687

Offset

0,6

Links

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

M. H. Albert, M. D. Atkinson and Robert Brignall, The enumeration of three pattern classes, arXiv:1206.3183 [math.CO] (2012), p. 18 (g.f. obtained from the Lemma 4.6).

Index entries for linear recurrences with constant coefficients, signature (14,-81,250,-444,458,-265,78,-9).

Formula

G.f.: x^4*(1-7*x+17*x^2-18*x^3+11*x^4-5*x^5)/((1-x)^2*(1-3*x)^2*(1-3*x+x^2)^2).

a(n) = 14*a(n-1) - 81*a(n-2) + 250*a(n-3) - 444*a(n-4) + 458*a(n-5) - 265*a(n-6) + 78*a(n-7) - 9*a(n-8). - Vincenzo Librandi, Dec 15 2012

Mathematica

CoefficientList[Series[x^4 (1 - 7 x + 17 x^2 - 18 x^3 + 11 x^4 - 5 x^5)/((1 - x)^2 (1 - 3 x)^2 (1 - 3 x + x^2)^2), {x, 0, 29}], x] (* Bruno Berselli, Nov 30 2012 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(1-7*x+17*x^2-18*x^3+11*x^4-5*x^5)/((1-x)^2*(1-3*x)^2*(1-3*x+x^2)^2), x, 0, n), x, n), n, 0, 29); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 1, 7, 34, 141, 537, 1942, 6786, 23143]; [n le 12 select I[n] else 14*Self(n-1) - 81*Self(n-2) + 250*Self(n-3) - 444*Self(n-4) + 458*Self(n-5) -265*Self(n-6) + 78*Self(n-7) - 9*Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 15 2012

Crossrefs

Cf. A219751-A219759, A219837.

Sequence in context: A319405 A122611 A326245 * A014915 A137747 A273722

Adjacent sequences: A219753 A219754 A219755 * A219757 A219758 A219759

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved