OFFSET
0,3
COMMENTS
With k=0 column added, becomes A094954.
Also, A(n,k) is the top-left element of the same 2 X 2 matrix raised to (k+1)-th power.
Also, A(n,k) is the denominator of the rational number which has continued fraction expansion consisting of k repeats of [1, n]. Example: the row (3, 11, 41, ...) is extracted from denominators of the continued fractions [0; 1, 2], [0; 1, 2, 1, 2], ... = 2/3, 8/11, ...
Also, A(n,k)=Product_{i=1..k} (n+2+2*cos(2*Pi*i/(2*k+1))). This is somehow connected to the diagonal product formulas for (2*k+1)-gons found by Steinbach.
Row sums of the triangle = A162998: (1, 3, 9, 29, 100, 369, 1458, ...).
LINKS
P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
EXAMPLE
The array begins:
1,...1,...1,....1,....1,.....1,.....1,...
2,...5,..13,...34,...89,...233....610,...
3,..11,..41,..153,..571,..2131,..........
4,..19,..91,..436,.2089,.................
5,..29,.169,..985,.......................
6,..41,.281,.............................
7,..55,..................................
8,.......................................
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jul 19 2009
EXTENSIONS
Spelling corrected by Jason G. Wurtzel, Aug 22 2010
Edited by Andrey Zabolotskiy, Sep 18 2017
STATUS
approved