|
Search: id:A102228
|
|
|
| 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. |
|
+0
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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Column 0 is A102227 shift left. Column 1 is A102229.
|
|
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).
|
|
PROGRAM
|
(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)[i-1, 1], B[i, j]=(A^2)[i-1, j]-(A^2)[i-1, j-1])); )); A=B); return((A^2)[n+1, k+1])}
|
|
CROSSREFS
|
Cf. A102225, A102226, A102227, A102229.
Sequence in context: A054098 A132089 A107880 this_sequence A141675 A021473 A035181
Adjacent sequences: A102225 A102226 A102227 this_sequence A102229 A102230 A102231
|
|
KEYWORD
|
sign,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jan 01 2005
|
|
|
Search completed in 0.002 seconds
|
