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#15 by Susanna Cuyler at Wed Dec 11 23:40:50 EST 2019
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#14 by Jon E. Schoenfield at Wed Dec 11 21:32:16 EST 2019
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#13 by Jon E. Schoenfield at Wed Dec 11 21:32:14 EST 2019
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| NAME
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Bisection of Fibonacci triangle A037027: odd -indexed members of column sequences of A037027 (not counting leading zeros).
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| COMMENTS
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Companion triangle (odd -indexed members) A060920.
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| FORMULA
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G.f. for column m >= 0: x^m*pFo(m+1, x)/(1-3*x+x^2)^(m+1), where pFo(n, x) := sum(Sum_{m=0..n-1} 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, Oct 11 2003
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| EXAMPLE
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{1}; {3,2}; {8,10,3}; {21,38,22,4}; ...; pFo(2,x)= ) = 2*(1-x).
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| STATUS
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approved
editing
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#12 by Joerg Arndt at Thu Mar 10 13:15:41 EST 2016
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#11 by Michel Marcus at Thu Mar 10 12:20:09 EST 2016
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#10 by Michel Marcus at Thu Mar 10 12:20:04 EST 2016
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| REFERENCES
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Yidong Sun, Numerical triangles and several classical sequences, Fib. Quart., Nov. 2005, pp. 359-370.
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| LINKS
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Yidong Sun, <a href="http://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.
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| FORMULA
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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.
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| STATUS
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approved
editing
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#9 by Charles R Greathouse IV at Fri May 10 12:44:45 EDT 2013
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| FORMULA
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G.f.: 1/(1-(3+2*y)*x+(1+y)^2*x^2). - ). - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Oct 11 2003
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Discussion
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| Fri May 10
| 12:44
| OEIS Server: https://oeis.org/edit/global/1911
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#8 by Russ Cox at Sat Mar 31 13:20:05 EDT 2012
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| AUTHOR
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_Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), _, Apr 20 2001
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Discussion
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| Sat Mar 31
| 13:20
| OEIS Server: https://oeis.org/edit/global/878
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#7 by N. J. A. Sloane at Sun Nov 13 11:40:32 EST 2011
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#6 by N. J. A. Sloane at Sun Nov 13 11:40:26 EST 2011
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| REFERENCES
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Yidong Sun, Numerical triangles and several classical sequences, Fib. Quart., Nov. 2005, pp. 359-370.
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| STATUS
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approved
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