A102098
Triangular matrix, read by rows, that satisfies: T(n,k) = [T^3](n-1,k) when n>k>=0, with T(n,n) = (n+1).
Original entry on oeis.org
1, 1, 2, 7, 8, 3, 139, 152, 27, 4, 5711, 6200, 999, 64, 5, 408354, 442552, 69687, 3904, 125, 6, 45605881, 49399320, 7724835, 416704, 11375, 216, 7, 7390305396, 8003532512, 1248465852, 66464960, 1725875, 27432, 343, 8, 1647470410551
Offset: 0
Rows of T begin:
[1],
[1,2],
[7,8,3],
[139,152,27,4],
[5711,6200,999,64,5],
[408354,442552,69687,3904,125,6],
[45605881,49399320,7724835,416704,11375,216,7],
[7390305396,8003532512,1248465852,66464960,1725875,27432,343,8],...
Matrix cube T^3 equals T excluding the main diagonal:
[1],
[7,8],
[139,152,27],
[5711,6200,999,64],
[408354,442552,69687,3904,125],...
-
{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]=j,if(j==1,B[i,j]=(A^3)[i-1,1], B[i,j]=(A^3)[i-1,j]));));A=B);return(A[n+1,k+1])}
A102100
Row sums of triangular matrix A102098, which shifts upward to exclude the main diagonal under matrix cube.
Original entry on oeis.org
1, 3, 18, 322, 12979, 924628, 103158338, 16710522378, 3724631345923, 1097090407192683, 413803244841678483, 194887616017161359389, 112265654949194591311618, 77751843768367000711311005
Offset: 0
-
{a(n)=local(A=matrix(2,2),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]=j,if(j==1,B[i,j]=(A^3)[i-1,1], B[i,j]=(A^3)[i-1,j]));));A=B); return(sum(k=0,n,A[n+1,k+1]))}
Original entry on oeis.org
0, 2, 4, 8, 40, 152, 1128, 6200, 61120, 442552, 5466320, 49399320, 735847800, 8003532512, 139910204080, 1784040237288, 35858685086352, 525504809786112, 11953187179149408, 198213959637435608, 5037776918810353960
Offset: 0
2 = 2*(1-2x) + 4*x*(1-2x) + 8*x^2*(1-2x)(1-3x) + 40*x^3*(1-2x)(1-3x)
+ 152*x^4*(1-2x)(1-3x)(1-4x) + 1128*x^5*(1-2x)(1-3x)(1-4x)
+ 6200*x^6*(1-2x)(1-3x)(1-4x)(1-5x) + 61120*x^7*(1-2x)(1-3x)(1-4x)(1-5x) +...
+ A102099(n+1)*x^(2n)*(1-2x)(1-3x)*..*(1-(n+2)x)
+ A102922(n+1)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+2)x) + ...
-
{a(n)=if(n==0,2,polcoeff(2-sum(k=0,n-1,a(k)*x^k*prod(j=2,k\2+2,1-j*x+x*O(x^n))),n))}
Showing 1-3 of 3 results.
Comments