A060923 - OEIS

A060923

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

1, 4, 1, 11, 17, 1, 29, 80, 39, 1, 76, 303, 315, 70, 1, 199, 1039, 1687, 905, 110, 1, 521, 3364, 7470, 6666, 2120, 159, 1, 1364, 10493, 29634, 37580, 20965, 4311, 217, 1, 3571, 31885, 109421, 181074, 148545

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..40.

FORMULA

a(n, m) = A060922(2*n-m, m).

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.

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.

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

EXAMPLE

Triangle begins:

{1};

{4,1};

{11,17,1};

{29,80,39,1};

...

pLe(2,x) = 1+11*x-11*x^2+4*x^3.

CROSSREFS

Row sums give A060926.

Column sequences (without leading zeros) are, for m=0..3: A002878, A060934-A060936.

Companion triangle A060924 (odd part).