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A060923 Bisection of Lucas triangle A060922: even-indexed members of column sequences of A060922 (not counting leading zeros).

%I A060923 #14 Mar 30 2024 13:24:17
%S A060923 1,4,1,11,17,1,29,80,39,1,76,303,315,70,1,199,1039,1687,905,110,1,521,
%T A060923 3364,7470,6666,2120,159,1,1364,10493,29634,37580,20965,4311,217,1,
%U A060923 3571,31885,109421,181074,148545
%N A060923 Bisection of Lucas triangle A060922: even-indexed members of column sequences of A060922 (not counting leading zeros).
%F A060923 a(n, m) = A060922(2*n-m, m).
%F A060923 a(n, m) = ((2*(n-m)+1)*A060924(n-1, m-1) + 2*(4*n-3*m)*a(n-1, m-1) + 4*(2*n-m-1)*A060924(n-2, m-1))/(5*m), m >= n >= 1; a(n, 0)= A002878(n); else 0.
%F A060923 G.f. for column m >= 0: x^m*pLe(m+1, x)/(1-3*x+x^2)^(m+1), where pLe(n, x) := Sum_{m=0..n+floor(n/2)} A061186(n, m)*x^m are the row polynomials of the (signed) staircase A061186.
%F A060923 T(n,k) = 3*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) + 2*T(n-2,k-1) - T(n-2,k-2) + 4*T(n-3,k-2), T(0,0) = 1, T(1,0) = 4, T(1,1) = 1, T(2,0) = 11, T(2,1) = 17, T(2,2) = 1, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Jan 21 2014
%e A060923 Triangle begins:
%e A060923   {1};
%e A060923   {4,1};
%e A060923   {11,17,1};
%e A060923   {29,80,39,1};
%e A060923   ...
%e A060923 pLe(2,x) = 1+11*x-11*x^2+4*x^3.
%Y A060923 Row sums give A060926.
%Y A060923 Column sequences (without leading zeros) are, for m=0..3: A002878, A060934-A060936.
%Y A060923 Companion triangle A060924 (odd part).
%Y A060923 Cf. A060922.
%K A060923 nonn,easy,tabl
%O A060923 0,2
%A A060923 _Wolfdieter Lang_, Apr 20 2001