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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130528 Triangle T, read by rows, where row n+1 of T equals row n of matrix power T^n added to row n of T (shifted right). 3
1, 1, 1, 2, 2, 1, 12, 8, 3, 1, 156, 80, 20, 4, 1, 3540, 1516, 300, 40, 5, 1, 123400, 46236, 7816, 840, 70, 6, 1, 6091988, 2054980, 309268, 28816, 1960, 112, 7, 1, 402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1, 34289884368, 9862677332 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..46.

EXAMPLE

Triangle begins:

1;

1, 1;

2, 2, 1;

12, 8, 3, 1;

156, 80, 20, 4, 1;

3540, 1516, 300, 40, 5, 1;

123400, 46236, 7816, 840, 70, 6, 1;

6091988, 2054980, 309268, 28816, 1960, 112, 7, 1;

402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1; ...

Matrix square T^2 begins:

1;

2, 1;

6, 4, 1;

38, 22, 6, 1;

480, 232, 52, 8, 1; ...

[Row 2 of T] = [row 1 of T^2, 0] + [0, row 1 of T]:

[2, 2, 1] = [2, 1, 0] + [0, 1, 1].

Matrix cube T^3 begins:

1;

3, 1;

12, 6, 1; ...

[Row 3 of T] = [row 2 of T^3, 0] + [0, row 2 of T]:

[12, 8, 3, 1] = [12, 6, 1, 0] + [0, 2, 2, 1].

Matrix 4th power T^4 begins:

1;

4, 1;

20, 8, 1;

156, 68, 12, 1; ...

[Row 4 of T] = [row 3 of T^4, 0] + [0, row 3 of T]:

[156, 80, 20, 4, 1] = [156, 68, 12, 1, 0] + [0, 12, 8, 3, 1].

PROG

(PARI) {T(n, k)=local(M=Mat(1)); if(n<k|k<0, 0, if(n==k, 1, M=matrix(n+1, n+1, r, c, if(n==k, 1, if(r>=c&r<=n, T(r-1, c-1)))); T(n-1, k-1)+(M^n)[n, k+1]))}

CROSSREFS

Columns: A130529, A130530, A130531.

Sequence in context: A014846 A100942 A132471 * A132986 A019112 A048660

Adjacent sequences:  A130525 A130526 A130527 * A130529 A130530 A130531

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jun 02 2007

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 02:25 EST 2016. Contains 278745 sequences.