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A321624 The Riordan square of the Lucas numbers, triangle read by rows, T(n, k) for 0 <= k <= n.

%I A321624 #19 Mar 27 2020 17:34:09
%S A321624 1,1,1,3,4,1,4,10,7,1,7,24,26,10,1,11,49,77,51,13,1,18,98,200,190,85,
%T A321624 16,1,29,187,473,595,390,128,19,1,47,350,1056,1658,1450,704,180,22,1,
%U A321624 76,642,2253,4255,4688,3062,1159,241,25,1
%N A321624 The Riordan square of the Lucas numbers, triangle read by rows, T(n, k) for 0 <= k <= n.
%C A321624 Compare A000032 (Lucas numbers with a(0) = 2), A000204 (Lucas numbers with a(0) undefined). Our variant has a(0) = 1.
%C A321624 Triangle, read by rows, given by [1, 2, -5/2, 1/2, 0, 0, 0, 0, 0, ...]DELTA[1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Feb 06 2020
%F A321624 T(0,0) = 1, T(1,1) = 1, T(1,0) = 1, T(n,k) = 0 for k<0 and for k>n, T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k) + 2*T(n-2,k-1), for n>1. - _Philippe Deléham_, Feb 06 2020
%e A321624 [0] [  1]
%e A321624 [1] [  1,    1]
%e A321624 [2] [  3,    4,    1]
%e A321624 [3] [  4,   10,    7,    1]
%e A321624 [4] [  7,   24,   26,   10,    1]
%e A321624 [5] [ 11,   49,   77,   51,   13,    1]
%e A321624 [6] [ 18,   98,  200,  190,   85,   16,    1]
%e A321624 [7] [ 29,  187,  473,  595,  390,  128,   19,   1]
%e A321624 [8] [ 47,  350, 1056, 1658, 1450,  704,  180,  22,   1]
%e A321624 [9] [ 76,  642, 2253, 4255, 4688, 3062, 1159, 241,  25, 1]
%p A321624 # The function RiordanSquare is defined in A321620.
%p A321624 Lucas :=  1 + x*(1 + 2*x)/(1 - x - x^2); RiordanSquare(Lucas, 10);
%t A321624 (* The function RiordanSquare is defined in A321620. *)
%t A321624 Lucas = 1 + x*(1 + 2*x)/(1 - x - x^2);
%t A321624 RiordanSquare[Lucas, 10] (* _Jean-François Alcover_, Jun 15 2019, from Maple *)
%o A321624 (Sage) # uses[riordan_square from A321620]
%o A321624 riordan_square(1 + x*(1 + 2*x)/(1 - x - x^2), 10)
%Y A321624 T(n, 0) = A000204, A000032 (Lucas), A321573 (row sums), A000007 (alternating row sums).
%Y A321624 Cf. A321620.
%K A321624 nonn,tabl
%O A321624 0,4
%A A321624 _Peter Luschny_, Nov 22 2018