OFFSET
0,7
LINKS
Paul D. Hanna, Rows n = 0..30, flattened.
FORMULA
EXAMPLE
This triangle T(n,k), where k=0..n(n+1)/2 in row n>=0, begins:
1;
(1),1;
(1),1,(1),2;
(1),1,2,(1),3,(1),5;
(1),1,2,4,(1),5,8,(1),9,(1),14;
(1),1,2,4,8,(1),9,14,22,(1),23,32,(1),33,(1),47;
(1),1,2,4,8,16,(1),17,26,40,62,(1),63,86,118,(1),119,152,(1),153,(1),200;
(1),1,2,4,8,16,32,(1),33,50,76,116,178,(1),179,242,328,446,(1),447,566,718,(1),719,872,(1),873,(1),1073;
...
where row n is equal to the partial sums of terms in row n-1, with 1's inserted at positions [0,n,2n-1,3n-3,4n-6,5n-10,...,n(n+1)/2-1].
The row sums and rightmost border form sequence A129867, which equals the row sums of triangle A130469.
Triangle A130469 begins:
1;
1, 1;
2, 2, 1;
6, 4, 3, 1;
24, 12, 6, 4, 1;
120, 48, 18, 8, 5, 1;
720, 240, 72, 24, 10, 6, 1; ...
which has the same row sums as this triangle.
PROG
(PARI) {T(n, k)=local(A=[1], B); for(m=0, n, t=0; B=[];
for(j=0, #A-1, if(j==t*m-t*(t+1)/2, t+=1; B=concat(B, 1)); B=concat(B, A[j+1]));
A=Vec( Ser(B)/(1-x+O(x^#B)) ) ); if(k+1>#A, 0, B[k+1])}
for(n=0, 12, for(k=0, n*(n+1)/2, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul D. Hanna, Dec 31 2010
STATUS
approved