A077843 - OEIS

%I #26 Feb 26 2020 15:12:04

%S 1,1,4,12,34,100,292,852,2488,7264,21208,61920,180784,527824,1541056,

%T 4499328,13136416,38353600,111978688,326937408,954539392,2786910976,

%U 8136775552,23756451840,69360276736,202507008256,591247473664,1726229517312,5039967998464

%N Expansion of (1-x)/(1-2*x-2*x^2-2*x^3).

%C Invert transform of the sequence 1,3,5,5,5,5,... which has g.f. (1+2x+2x^2)/(1-x). - _Paul Barry_, Mar 01 2011

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,2).

%F a(n) = sum(k=1..n, sum(i=k..n,(sum(j=0..k, binomial(j,-3*k+2*j+i)*2^(-2*k+j+i)* binomial(k,j)))*binomial(n+k-i-1,k-1))). - _Vladimir Kruchinin_, May 05 2011

%e Eigensequence of the triangle

%e   1,

%e   3, 1,

%e   5, 3, 1,

%e   5, 5, 3, 1,

%e   5, 5, 5, 3, 1,

%e   5, 5, 5, 5, 3, 1,

%e   5, 5, 5, 5, 5, 3, 1,

%e   5, 5, 5, 5, 5, 5, 3, 1,

%e   ...

%e - _Paul Barry_, Mar 01 2011

%o (Sage)

%o from sage.combinat.sloane_functions import recur_gen3

%o it = recur_gen3(0,1,1,2,2,2)

%o [next(it) for i in range(35)] # _Zerinvary Lajos_, Jun 25 2008

%o (Maxima)

%o a(n):=sum(sum((sum(binomial(j,-3*k+2*j+i)*2^(-2*k+j+i)*binomial(k,j),j,0,k))*binomial(n+k-i-1,k-1),i,k,n),k,1,n); /* _Vladimir Kruchinin_, May 05 2011 */

%o (PARI) Vec((1-x)/(1-2*x-2*x^2-2*x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Nov 17 2002