A091351
Triangle T, read by rows, such that T(n,k) equals the (n-k)-th row sum of T^k, where T^k is the k-th power of T as a lower triangular matrix.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 9, 4, 1, 1, 24, 30, 16, 5, 1, 1, 77, 115, 70, 25, 6, 1, 1, 295, 510, 344, 135, 36, 7, 1, 1, 1329, 2602, 1908, 805, 231, 49, 8, 1, 1, 6934, 15133, 11904, 5325, 1616, 364, 64, 9, 1, 1, 41351, 99367, 83028, 39001, 12381, 2919, 540, 81, 10, 1
Offset: 0
T(7,3) = 344 = 1*1 + 9*3 + 9*9 + 4*30 + 1*115
= T(4,0)*T(2,2) +T(4,1)*T(3,2) +T(4,2)*T(4,2) +T(4,3)*T(5,2) +T(4,4)*T(6,2).
Rows begin:
{1},
{1,1},
{1,2,1},
{1,4,3,1},
{1,9,9,4,1},
{1,24,30,16,5,1},
{1,77,115,70,25,6,1},
{1,295,510,344,135,36,7,1},
{1,1329,2602,1908,805,231,49,8,1},
{1,6934,15133,11904,5325,1616,364,64,9,1},...
-
T(n,k)=if(k>n || n<0 || k<0,0,if(k==0 || k==n,1, sum(j=0,n-k,T(n-k,j)*T(j+k-1,k-1)););)
A091352
Row sums of triangle A091351, in which the k-th column lists the row sums of the k-th power of A091351 (when considered as a lower triangular matrix).
Original entry on oeis.org
1, 2, 4, 9, 24, 77, 295, 1329, 6934, 41351, 278680, 2101434, 17574552, 161740316, 1626733108, 17771416521, 209739328924, 2661301094008, 36148700652163, 523597247829867, 8059284921781892, 131408547139817541
Offset: 0
A104445
Triangular matrix T, read by rows, that satisfies: SHIFT_LEFT_UP(T) = T^2 - T + I, or, equivalently: T(n+1,k+1) = [T^2](n,k) - T(n,k) + [T^0](n,k) for n>=k>=0, with T(0,0)=1.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 9, 9, 4, 1, 1, 1, 24, 30, 16, 5, 1, 1, 1, 77, 115, 70, 25, 6, 1, 1, 1, 295, 510, 344, 135, 36, 7, 1, 1, 1, 1329, 2602, 1908, 805, 231, 49, 8, 1, 1, 1, 6934, 15133, 11904, 5325, 1616, 364, 64, 9, 1, 1, 1, 41351, 99367, 83028, 39001
Offset: 0
Rows begin:
1;
1,1;
1,1,1;
1,2,1,1;
1,4,3,1,1;
1,9,9,4,1,1;
1,24,30,16,5,1,1;
1,77,115,70,25,6,1,1;
1,295,510,344,135,36,7,1,1;
1,1329,2602,1908,805,231,49,8,1,1;
1,6934,15133,11904,5325,1616,364,64,9,1,1; ...
A091354
Row sums of the matrix cube of triangle A091351, in which the k-th column lists the row sums of A091351^k (the k-th power of A091351 when considered as a lower triangular matrix).
Original entry on oeis.org
1, 4, 16, 70, 344, 1908, 11904, 83028, 642960, 5490560, 51373420, 523581128, 5781166688, 68819889018, 879350377816, 12012238559559, 174794145558664, 2700485871440464, 44163954923956850, 762460145368056070
Offset: 0
A104447
Column 1 of triangular matrix A104446.
Original entry on oeis.org
1, 2, 5, 13, 39, 139, 587, 2897, 16462, 106301, 771313, 6228073, 55494336, 541651873, 5753940704, 66147591142, 818802488476, 10864622564915, 153914784829775, 2319599022540318, 37068215129072522, 626279667948552452
Offset: 0
-
a(n)=local(A=Mat(1),B);for(m=1,n+1,B=A^2-A+A^0; A=matrix(m+1,m+1);for(i=1,m+1, for(j=1,i, if(i<2 || j==i,A[i,j]=1,if(j==1,A[i,j]=1,A[i,j]=B[i-1,j-1]))))); return((A^2)[n+2,2])
Showing 1-5 of 5 results.
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