A262593 - OEIS

%I #10 Oct 24 2015 12:32:50

%S 1,-1,-3,-1,13,63,237,879,3357,13135,52061,207519,829037,3314719,

%T 13256973,53025423,212098557,848390319,3393556477,13574220095,

%U 54296873421,217187485439,868749932077,3474999717039,13899998855133,55599995405583,222399981605277,889599926401759,3558399705585197

%N Expansion of (1-3*x)^3/((1-x)^4*(1-4*x)).

%C Suggested by A262592.

%H Colin Barker, <a href="/A262593/b262593.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,28,-17,4).

%F a(n + 1) = (1/3)*(12*a(n) - 4*n^3 + 18*n^2 + 4*n - 15), a(0) = 1. - _Ilya Gutkovskiy_, Oct 22 2015

%F From _Colin Barker_, Oct 23 2015: (Start)

%F a(n) = 8*a(n-1)-22*a(n-2)+28*a(n-3)-17*a(n-4)+4*a(n-5) for n>4.

%F a(n) = (77+4^(1+n)-84*n-126*n^2+36*n^3)/81.

%F (End)

%o (PARI) Vec((1-3*x)^3/((1-x)^4*(1-4*x)) + O(x^40)) \\ _Michel Marcus_, Oct 23 2015

%o (PARI) a(n) = (77+4^(1+n)-84*n-126*n^2+36*n^3)/81 \\ _Colin Barker_, Oct 23 2015

%Y Cf. A262592.

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, Oct 22 2015