A026998 - OEIS

%I #10 Mar 30 2012 18:56:13

%S 1,1,1,1,4,1,1,4,8,1,1,4,11,13,1,1,4,11,26,19,1,1,4,11,29,54,26,1,1,4,

%T 11,29,73,101,34,1,1,4,11,29,76,171,174,43,1,1,4,11,29,76,196,370,281,

%U 53,1,1,4,11,29,76,199,487,743,431,64,1,1,4

%N Triangular array T read by rows: T(n,k)=t(n,2k), t given by A027960, 0<=k<=n, n >= 0.

%C Right-edge columns are polynomials approximating Lucas(2n+1).

%F T(n, k) = Lucas(2n+1) = A002878(n) for 2k<=n, otherwise the (2n-2k)th coefficient of the power series for (1+2x)/{(1-x-x^2)(1-x)^(2k-n)}.

%e ............................1

%e ..........................1,1

%e ........................1,4,1

%e ......................1,4,8,1

%e ..................1,4,11,13,1

%e ...............1,4,11,26,19,1

%e ............1,4,11,29,54,26,1

%e ........1,4,11,29,73,101,34,1

%e ....1,4,11,29,76,171,174,43,1

%e 1,4,11,29,76,196,370,281,53,1

%Y This is a bisection of the "Lucas array" A027960, see A027011 for the other bisection.

%Y Row sums are in A000918. Right-edge columns include A034856, A027966, A027968, A027970, A027972.

%K nonn,tabl

%O 0,5

%A _Clark Kimberling_

%E Edited by _Ralf Stephan_, May 05 2005