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A060921
Bisection of Fibonacci triangle A037027: odd-indexed members of column sequences of A037027 (not counting leading zeros).
10
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
0,2
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.
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
EXAMPLE
{1}; {3,2}; {8,10,3}; {21,38,22,4}; ...; pFo(2,x) = 2*(1-x).
CROSSREFS
Sequence in context: A214683 A371998 A363816 * A163356 A209360 A095013
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Apr 20 2001
STATUS
approved