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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138271 Triangle T, read by rows, where column k of T = column 0 of T^(k+1) for k>0, with column 0 of T = column 0 of T^4 shift right. 4
1, 1, 1, 4, 2, 1, 28, 10, 3, 1, 268, 78, 18, 4, 1, 3164, 798, 156, 28, 5, 1, 43672, 9874, 1714, 268, 40, 6, 1, 682632, 141282, 22368, 3164, 420, 54, 7, 1, 11834536, 2273730, 333910, 43672, 5320, 618, 70, 8, 1, 224283416, 40400466, 5566728, 682632, 77720 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..49.

FORMULA

Column k of T^(j+1) = column j of T^(k+1) for j>=0, k>=0.

EXAMPLE

Triangle T begins:

1;

1, 1;

4, 2, 1;

28, 10, 3, 1;

268, 78, 18, 4, 1;

3164, 798, 156, 28, 5, 1;

43672, 9874, 1714, 268, 40, 6, 1;

682632, 141282, 22368, 3164, 420, 54, 7, 1;

11834536, 2273730, 333910, 43672, 5320, 618, 70, 8, 1;

224283416, 40400466, 5566728, 682632, 77720, 8378, 868, 88, 9, 1; ...

where column k of T = column 0 of T^(k+1)

with column 0 of T = column 0 of T^4 shift right:

column 1 of T = column 0 of T^2;

column 2 of T = column 0 of T^3;

column 3 of T = column 0 of T^4.

Matrix square of T, T^2, begins:

1;

2, 1;

10, 4, 1;

78, 26, 6, 1;

798, 232, 48, 8, 1;

9874, 2578, 486, 76, 10, 1;

141282, 33764, 5888, 864, 110, 12, 1;

2273730, 503910, 82210, 11396, 1390, 150, 14, 1; ...

where column k of T^2 = column 1 of T^(k+1):

column 0 of T^2 = column 1 of T;

column 2 of T^2 = column 1 of T^3;

column 3 of T^2 = column 1 of T^4.

Matrix cube of T, T^3, begins:

1;

3, 1;

18, 6, 1;

156, 48, 9, 1;

1714, 486, 90, 12, 1;

22368, 5888, 1050, 144, 15, 1;

333910, 82210, 14046, 1908, 210, 18, 1;

5566728, 1289928, 211182, 28072, 3120, 288, 21, 1; ...

where column k of T^3 = column 2 of T^(k+1):

column 0 of T^3 = column 2 of T;

column 1 of T^3 = column 2 of T^2;

column 3 of T^3 = column 2 of T^4.

Matrix 4th power of T, T^4, begins:

1;

4, 1;

28, 8, 1;

268, 76, 12, 1;

3164, 864, 144, 16, 1;

43672, 11396, 1908, 232, 20, 1;

682632, 170000, 28072, 3520, 340, 24, 1;

11834536, 2814832, 454848, 57408, 5820, 468, 28, 1; ...

where column k of T^4 = column 3 of T^(k+1):

column 0 of T^4 = column 3 of T = column 0 of T shift left;

column 1 of T^4 = column 3 of T^2;

column 2 of T^4 = column 3 of T^3.

PROG

(PARI) {T(n, k) = if(k>n||k<0, 0, if(k==n, 1, if(k==0, T(n+2, 3), sum(j=0, n-k, T(n-k, j)*T(j+k-1, k-1))); ); )}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

(PARI) /* Column k of T = column 0 of T^(k+1): */

{T(n, k) = local(M=if(n==0, Mat(1), matrix(n, n, r, c, if(r>=c, T(r-1, c-1))))); if(k==n, 1, if(k==0, (M^4)[n, 1], (M^(k+1))[n-k+1, 1]))}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. columns: A138272, A138273, A138274; central terms: A138275; variants: A091351, A094587, A135902.

Sequence in context: A158835 A236961 A245958 * A136212 A136215 A136737

Adjacent sequences:  A138268 A138269 A138270 * A138272 A138273 A138274

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Mar 11 2008

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 November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)