A219759 Expansion of x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6).

0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906, 102187, 323053, 984354, 2908671, 8375521, 23594410, 65237027, 177520325, 476515378, 1264297431, 3321423193, 8653113914, 22386784603, 57586262493, 147447786562, 376173191919, 957113924753, 2430649701066

Offset

0,5

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. 30.

Index entries for linear recurrences with constant coefficients, signature (16,-112,449,-1132,1852,-1952,1264,-448,64).

Formula

G.f.: x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6).

Maple

A219759 := proc(n)
    if n <= 1 then
        0;
    else
        2^n*(881*n^2/24-14393*n/60+137+7*n^4/24-49*n^3/8+n^5/120) -384+ 64*A001906(n+2) ;
        %/64 ;
    end if;
end proc:
seq(A219759(n), n=0..20) ; # R. J. Mathar, Aug 19 2022

Mathematica

CoefficientList[Series[x^4 (2 - 12 x + 24 x^2 - 8 x^3 - 41 x^4 + 57 x^5 - 16 x^6)/((1 - x) (1 - 3 x + x^2) (1 - 2 x)^6), {x, 0, 28}], x] (* Bruno Berselli, Nov 30 2012 *)
LinearRecurrence[{16, -112, 449, -1132, 1852, -1952, 1264, -448, 64}, {0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906}, 40] (* Harvey P. Dale, Mar 01 2023 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6), x, 0, n), x, n), n, 0, 28); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906, 102187, 323053]; [n le 11 select I[n] else 16*Self(n-1) -112*Self(n-2) + 449*Self(n-3) - 1132*Self(n-4) + 1852*Self(n-5) - 1952*Self(n-6) + 1264*Self(n-7) - 448*Self(n-8) + 64*Self(n-9): n in [1..30]]; // Vincenzo Librandi, Dec 14 2012

Crossrefs

Cf. A219751-A219758, A219837.

Sequence in context: A278772 A213432 A219837 * A196797 A196585 A197042

Adjacent sequences: A219756 A219757 A219758 * A219760 A219761 A219762

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved