A219837 Expansion of x^4*(2-10*x+18*x^2-7*x^3-21*x^4+25*x^5-x^6)/((1-x)^3*(1-2*x)^6).

0, 0, 0, 0, 2, 20, 120, 567, 2320, 8596, 29578, 96058, 297776, 888460, 2567534, 7221974, 19849284, 53473464, 141559090, 369018290, 948897336, 2410350276, 6055659350, 15063123950, 37130340492, 90769197360, 220209351130, 530489281162, 1269657766720

Offset

0,5

Links

Bruno Berselli, 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. 28.

Index entries for linear recurrences with constant coefficients, signature (15,-99,377,-912,1452,-1520,1008,-384,64).

Formula

G.f.: x^4*(2-12*x+28*x^2-25*x^3-14*x^4+46*x^5-26*x^6+x^7)/((1-x)^4*(1-2*x)^6) = x^4*(2-10*x+18*x^2-7*x^3-21*x^4+25*x^5-x^6)/((1-x)^3*(1-2*x)^6) (the first formula is in the paper indicated in Link section).

a(n) = 2^(n-10)*(n^5-16*n^4+547*n^3-7976*n^2+55660*n-158832)/3+(3*n+17)*n+52 with n>1, a(0)=a(1)=0.

Mathematica

CoefficientList[Series[x^4 (2 - 10 x + 18 x^2 - 7 x^3 - 21 x^4 + 25 x^5 - x^6)/((1 - x)^3 (1 - 2 x)^6), {x, 0, 28}], x]
LinearRecurrence[{15, -99, 377, -912, 1452, -1520, 1008, -384, 64}, {0, 0, 0, 0, 2, 20, 120, 567, 2320, 8596, 29578}, 30] (* Harvey P. Dale, Dec 03 2020 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(2-10*x+18*x^2-7*x^3-21*x^4+25*x^5-x^6)/((1-x)^3*(1-2*x)^6), x, 0, n), x, n), n, 0, 28);
(Magma) I:=[0, 0, 0, 0, 2, 20, 120, 567, 2320, 8596, 29578, 96058, 297776]; [n le 11 select I[n] else 15*Self(n-1) - 99*Self(n-2) + 377*Self(n-3) - 912*Self(n-4) + 1452*Self(n-5) - 1520*Self(n-6) + 1008*Self(n-7) - 384*Self(n-8) + 64*Self(n-9): n in [1..30]]; // Vincenzo Librandi, Dec 14 2012

Crossrefs

Cf. A219751-A219759.

Sequence in context: A061004 A278772 A213432 * A219759 A196797 A196585

Adjacent sequences: A219834 A219835 A219836 * A219838 A219839 A219840

Keyword

nonn,easy

Author

Bruno Berselli, Nov 29 2012

Status

approved