

A102426


Triangle read by rows giving coefficients of polynomials defined by F(0)=0, F(1)=1, F(n+1) = F(n) + x*F(n1).


10



0, 1, 1, 1, 1, 2, 1, 1, 3, 1, 3, 4, 1, 1, 6, 5, 1, 4, 10, 6, 1, 1, 10, 15, 7, 1, 5, 20, 21, 8, 1, 1, 15, 35, 28, 9, 1, 6, 35, 56, 36, 10, 1, 1, 21, 70, 84, 45, 11, 1, 7, 56, 126, 120, 55, 12, 1, 1, 28, 126, 210, 165, 66, 13, 1, 8, 84, 252, 330, 220, 78, 14, 1, 1, 36, 210, 462, 495, 286, 91
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OFFSET

0,6


COMMENTS

Essentially the same as A098925: a(0)=0 followed by A098925. [R. J. Mathar, Aug 30 2008]
F(n) + 2x * F(n1) gives Lucas polynomials (cf. A034807).  Maxim Krikun (krikun(AT)iecn.unancy.fr), Jun 24 2007
After the initial 0, these are the nonzero coefficients of the Fibonacci polynomials; see the Mathematica section.  Clark Kimberling, Oct 10 2013


REFERENCES

H.H. Chern, H.K. Hwang, T.H. Tsai, Random unfriendly seating arrangement in a dining table, arXiv preprint arXiv:1406.0614, 2014
Dominique Foata and GuoNiu Han, Multivariable tangent and secant qderivative polynomials, Manuscript, Mar 21 2012


LINKS

Table of n, a(n) for n=0..79.
G. Hetyei, Hurwitzian continued fractions containing a repeated constant and an arithmetic progression, arXiv preprint arXiv:1211.2494, 2012.  From N. J. A. Sloane, Jan 02 2013


FORMULA

Alternatively, as n is even or odd: T(n2, k) + T(n1, k1) = T(n, k), T(n2, k) + T(n1, k) = T(n, k)
T(n, k)=binomial(floor(n/2)+k, floor((n1)/2k) )  Paul Barry, Jun 22 2005


EXAMPLE

The first few polynomials are:
0
1
1
x + 1
2x + 1
x^2 + 3x + 1
3x^2 + 4x + 1


MATHEMATICA

Table[Fibonacci[n, x], {n, 0, 10}] (* Clark Kimberling, Oct 10 2013 *)


CROSSREFS

Upward diagonals sums are A062200. Downward rows are A102427. Row sums are A000045. Row terms reversed = A011973. Also A102427, A102428, A102429.
All of A011973, A092865, A098925, A102426, A169803 describe essentially the same triangle in different ways.
Sequence in context: A035667 A092865 A098925 * A052920 A089141 A245717
Adjacent sequences: A102423 A102424 A102425 * A102427 A102428 A102429


KEYWORD

easy,nonn,tabf


AUTHOR

Russell Walsmith, Jan 08 2005


STATUS

approved



