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A060923 Bisection of Lucas triangle A060922: even indexed members of column sequences of A060922 (not counting leading zeros). 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums give A060926. Column sequences (without leading zeros) are, for m=0..3: A002878, A060934-6.

Companion triangle A060924 (odd part).

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(A061186(n, m)*x^m, m=0..n+floor(n/2)) 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

{1}; {4,1}; {11,17,1}; {29,80,39,1}; ...; pLe(2,x)= 1+11*x-11*x^2+4*x^3.

CROSSREFS

Sequence in context: A135552 A181690 A109088 * A298362 A143952 A097877

Adjacent sequences:  A060920 A060921 A060922 * A060924 A060925 A060926

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 20 2001

STATUS

approved

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)