A187695 - OEIS

%I #29 Nov 15 2024 18:05:53

%S 0,0,0,0,1,26,264,1846,10616,54354,258388,1168862,5109696,21805162,

%T 91460972,378874998,1555269016,6341845250,25732834116,104034429454,

%U 419461348976,1687846763418,6781455643420,27216164395430,109135969307976,437358413244466,1751878519306484,7014851306040126,28081422396752416

%N G.f.: x^4*(1+x)*(1+12*x-31*x^2+12*x^2)/((1-x)^2*(1-2*x)^2*(1-3*x)*(1-4*x)).

%H Vincenzo Librandi, <a href="/A187695/b187695.txt">Table of n, a(n) for n = 0..1000</a>

%H F. Bergeron, M. Bousquet-Mélou and S. Dulucq, <a href="http://www.labmath.uqam.ca/~annales/volumes/19-2/PDF/139-151.pdf">Standard paths in the composition poset</a>, Ann. Sci. Math. Quebec, 19 (1995), no. 2, 139-151.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (13,-67,175,-244,172,-48).

%F a(n) = 27*2^(n-4)*n + 33*2^(n-4) - 2*n + 2 - 26*3^(n-2)+25*4^(n-3), n>1. - _R. J. Mathar_, Mar 17 2011

%F E.g.f.: (-901 -228*x + 1152*(1-x)*exp(x) + (1188 + 1944*x)*exp(2*x) - 1664*exp(3*x) + 225*exp(4*x))/576. - _G. C. Greubel_, Nov 06 2018

%t Join[{0,0}, LinearRecurrence[{13,-67,175,-244,172,-48},{0,0,1,26,264, 1846}, 30]] (* _Harvey P. Dale_, Mar 02 2015 *)

%o (Maxima) makelist(coeff(taylor(x^4*(1+x)*(1+12*x-31*x^2+12*x^2)/((1-x)^2*(1-2*x)^2*(1-3*x)*(1-4*x)),x,0,n),x,n),n,0,28); /* _Bruno Berselli_, May 30 2011 */

%o (Magma) [0,0] cat [27*2^(n-4)*n +33*2^(n-4)-2*n+2-26*3^(n-2)+25*4^(n-3): n in [2..30]]; // _Vincenzo Librandi_, Feb 19 2012

%o (PARI) concat([0,0], vector(30, n, n++; 27*2^(n-4)*n +33*2^(n-4)-2*n+2-26*3^(n-2)+25*4^(n-3))) \\ _G. C. Greubel_, Nov 06 2018

%Y Cf. A187693.

%K nonn

%O 0,6

%A _N. J. A. Sloane_, Mar 12 2011