|
Search: id:A060921
|
|
|
| A060921 |
|
Bisection of Fibonacci triangle A037027: odd indexed members of column sequences of A037027 (not counting leading zeros). |
|
+0
11
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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.
|
|
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(A061177(n-1, m)*x^m, m=0..n-1) (row polynomials of signed triangle A061177).
G.f.: 1/(1-(3+2*y)*x+(1+y)^2*x^2). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 11 2003
|
|
EXAMPLE
|
{1}; {3,2}; {8,10,3}; {21,38,22,4}; ...; pFo(2,x)= 2*(1-x).
|
|
CROSSREFS
|
Adjacent sequences: A060918 A060919 A060920 this_sequence A060922 A060923 A060924
Sequence in context: A057163 A130918 A021308 this_sequence A095013 A094188 A088551
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 20 2001
|
|
|
Search completed in 0.002 seconds
|
