

A102228


Triangular matrix, read by rows, equal to the matrix square of A102225, such that the first differences of row k forms row (k+1) of A102225.


5



1, 2, 1, 3, 2, 1, 7, 13, 6, 1, 17, 34, 23, 10, 1, 75, 214, 224, 121, 22, 1, 346, 1080, 1361, 712, 55, 42, 1, 4874, 17748, 26541, 19615, 6616, 1097, 86, 1, 49047, 210687, 319527, 200868, 71593, 32024, 1289, 170, 1, 3009094, 12958931, 22536661, 19799672, 9144014, 2280135, 311880
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OFFSET

0,2


COMMENTS

Column 0 is A102227 shift left. Column 1 is A102229.


LINKS

Table of n, a(n) for n=0..51.


FORMULA

T(n, k) = Sum_{j=0..k} A102225(n+1, j) for n>k>0, with T(n, n)=1 for n>=0 and T(n, 0) = A102226(n+1) for n>=0.


EXAMPLE

Rows begin:
[1],
[2,1],
[3,2,1],
[7,13,6,1],
[17,34,23,10,1],
[75,214,224,121,22,1],
[346,1080,1361,712,55,42,1],
[4874,17748,26541,19615,6616,1097,86,1],...
Equals the matrix square of A102225, which starts:
[1],
[1,1],
[2,1,1],
[3,5,3,1],
[7,20,19,5,1],
[17,51,57,33,11,1],...
Each row k of A102228 equals the partial sums of
row (k+1) of A102225 (prior to main diagonal term).


PROG

(PARI) {T(n, k)=local(A=matrix(1, 1), B); A[1, 1]=1; for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, 1]=(A^2)[i1, 1], B[i, j]=(A^2)[i1, j](A^2)[i1, j1])); )); A=B); return((A^2)[n+1, k+1])}


CROSSREFS

Cf. A102225, A102226, A102227, A102229.
Sequence in context: A185624 A162387 A107880 * A141675 A021473 A035181
Adjacent sequences: A102225 A102226 A102227 * A102229 A102230 A102231


KEYWORD

sign,tabl


AUTHOR

Paul D. Hanna, Jan 01 2005


STATUS

approved



