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

1, 3, 2, 8, 10, 3, 21, 38, 22, 4, 55, 130, 111, 40, 5, 144, 420, 474, 256, 65, 6, 377, 1308, 1836, 1324, 511, 98, 7, 987, 3970, 6666, 6020, 3130, 924, 140, 8, 2584, 11822, 23109, 25088, 16435, 6588, 1554, 192, 9

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• nonn
• easy
• tabl

Comments

Row sums give A002450. Column sequences (without leading zeros) give for m=0..5: A001906, 2*A001870, A061182, 4*A061183, A061184, 2*A061185.

Companion triangle (odd-indexed members) A060920.

Examples

			{1}; {3,2}; {8,10,3}; {21,38,22,4}; ...; pFo(2,x) = 2*(1-x).
		

Links

• Yidong Sun, Numerical Triangles and Several Classical Sequences, Fib. Quart. 43, no. 4, Nov. 2005, pp. 359-370.

Formula

a(n, m) = A037027(2*n+1-m, m).

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.

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).

G.f.: 1/(1 - (3+2*y)*x + (1+y)^2*x^2). - Vladeta Jovovic, Oct 11 2003