cp's OEIS Frontend

A140071 Triangle read by rows: iterates of X * [1,0,0,0,...]; where X = an infinite lower bidiagonal matrix with [3,1,3,1,3,1...] in the main diagonal and [1,1,1,...] in the subdiagonal.

%I A140071 #8 Feb 17 2014 18:11:41
%S A140071 1,3,1,9,4,1,27,13,7,1,81,40,34,8,1,243,121,142,42,11,1,729,364,547,
%T A140071 184,75,12,1,2187,1093,2005,731,409,87,15,1,6561,3280,7108,2736,1958,
%U A140071 496,132,16,1,19683,9841,24604,9844,8610,2454,892,148,19,1
%N A140071 Triangle read by rows: iterates of X * [1,0,0,0,...]; where X = an infinite lower bidiagonal matrix with [3,1,3,1,3,1...] in the main diagonal and [1,1,1,...] in the subdiagonal.
%C A140071 Companion triangle A140070 uses an analogous operation with the main diagonal [1,3,1,3,1,3,...].
%F A140071 From _Peter Bala_, Jan 17 2014: (Start)
%F A140071 O.g.f. (1 + (x - 1)*z)/(1 - 4*z - (x^2 - 3)*z^2) = 1 + (x + 3)*z + (x^2 + 4*x + 9)*z^2 + ....
%F A140071 Recurrence equation: T(n,k) = 4*T(n-1,k) - 3*T(n-2,k) + T(n-2,k-2).
%F A140071 Recurrence equation for row polynomials: R(n,x) = 4*R(n-1,x) + (x^2 - 3)*R(n-2,x) with R(0,x) = 1 and R(1,x) = 3 + x.
%F A140071 Another recurrence equation: R(n,x) = (x + 2)*R(n-1,x) + R(n-1,-x) with R(0,x) = 1. Cf. A157751. (End)
%e A140071 First few rows of the triangle are:
%e A140071 1;
%e A140071 3, 1;
%e A140071 9, 4, 1;
%e A140071 27, 13, 7, 1;
%e A140071 81, 40, 34, 8, 1;
%e A140071 243, 121, 142, 42, 11, 1;
%e A140071 729, 364, 547, 184, 75, 12, 1;
%e A140071 2187, 1093, 2005, 731, 409, 87, 15, 1;
%e A140071 6561, 3280, 7108, 2736, 1958, 496, 132, 16, 1;
%e A140071 ...
%Y A140071 Cf. A140070, A007070 (row sums), A157751.
%K A140071 nonn,tabl
%O A140071 1,2
%A A140071 _Gary W. Adamson_ and _Roger L. Bagula_, May 04 2008