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

0,2

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

Table of n, a(n) for n=0..44.

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

Adjacent sequences: A060918 A060919 A060920 * A060922 A060923 A060924

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Apr 20 2001

Status

approved