login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101161 A number triangle associated with the Chebyshev polynomials of the first kind. 2
1, 2, 1, 2, 3, 1, 2, 7, 4, 1, 2, 18, 14, 5, 1, 2, 47, 52, 23, 6, 1, 2, 123, 194, 110, 34, 7, 1, 2, 322, 724, 527, 198, 47, 8, 1, 2, 843, 2702, 2525, 1154, 322, 62, 9, 1, 2, 2207, 10084, 12098, 6726, 2207, 488, 79, 10, 1, 2, 5778, 37634, 57965, 39202, 15127, 3842, 702, 98 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A101162. Diagonal sums are A101163.

LINKS

Table of n, a(n) for n=0..63.

Index entries for sequences related to Chebyshev polynomials.

FORMULA

Number triangle S(n, k)=if(n=k, 1, 2T(n-k, (k+2)/2)) where T(n, k)=(n/2)sum{j=0..floor(n/2), C(n-j, j)(-1)^j*(2k)^(n-2j)};or S(n, k)=if(k<n, sum{j=0..n, C(n-k+j, 2j)(2(n-k)/(n-k+j))k^j}, if(k=n, 1, 0)) Columns have g.f. (1-x^2)x^k/(1-(k+2)x+x^2). Also square array if(n=0, 1, 2T(n, (k+2)/2) read by antidiagonals.

EXAMPLE

Rows begin {1}, {2,1}, {2,3,1}, {2,7,4,1}, {2,18,14,5,1},...

As a square array, rows begin

1,1,1,1,1,...

2,3,4,5,6,...

2,7,14,23,34,...

2,18,52,110,198,...

2,47,194,527,1154,...

CROSSREFS

Sequence in context: A263714 A263703 A263752 * A245049 A214261 A097825

Adjacent sequences:  A101158 A101159 A101160 * A101162 A101163 A101164

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Dec 02 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 21 21:34 EDT 2019. Contains 321382 sequences. (Running on oeis4.)