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A060921 Bisection of Fibonacci triangle A037027: odd-indexed members of column sequences of A037027 (not counting leading zeros).

%I A060921 #17 Jan 05 2025 19:51:36
%S A060921 1,3,2,8,10,3,21,38,22,4,55,130,111,40,5,144,420,474,256,65,6,377,
%T A060921 1308,1836,1324,511,98,7,987,3970,6666,6020,3130,924,140,8,2584,11822,
%U A060921 23109,25088,16435,6588,1554,192,9
%N A060921 Bisection of Fibonacci triangle A037027: odd-indexed members of column sequences of A037027 (not counting leading zeros).
%C A060921 Row sums give A002450. Column sequences (without leading zeros) give for m=0..5: A001906, 2*A001870, A061182, 4*A061183, A061184, 2*A061185.
%C A060921 Companion triangle (odd-indexed members) A060920.
%H A060921 Yidong Sun, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/43-4/paper43-4-10b.pdf">Numerical Triangles and Several Classical Sequences</a>, Fib. Quart. 43, no. 4, Nov. 2005, pp. 359-370.
%F A060921 a(n, m) = A037027(2*n+1-m, m).
%F A060921 a(n, m) = (2*(n-m+1)*A060920(n, m-1)+2*(2*n+1)*a(n-1, m-1))/(5*m), n >= m>0; a(n, 0) := S(n, 3)=A001906(n+1) with Chebyshev's S(n, x) polynomials A049310; else 0.
%F A060921 G.f. for column m >= 0: x^m*pFo(m+1, x)/(1-3*x+x^2)^(m+1), where pFo(n, x) := Sum_{m=0..n-1} A061177(n-1, m)*x^m (row polynomials of signed triangle A061177).
%F A060921 G.f.: 1/(1 - (3+2*y)*x + (1+y)^2*x^2). - _Vladeta Jovovic_, Oct 11 2003
%e A060921 {1}; {3,2}; {8,10,3}; {21,38,22,4}; ...; pFo(2,x) = 2*(1-x).
%K A060921 nonn,easy,tabl
%O A060921 0,2
%A A060921 _Wolfdieter Lang_, Apr 20 2001