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.

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

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)[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: A185624 A162387 A107880 * A141675 A248809 A021473

Adjacent sequences: A102225 A102226 A102227 * A102229 A102230 A102231

Keyword

sign,tabl

Author

Paul D. Hanna, Jan 01 2005

Status

approved