cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A136223 Column 2 of triangle A136220; also equals column 0 of U^3 = A136236 where U = A136228.

Original entry on oeis.org

1, 3, 21, 208, 2637, 40731, 742620, 15624420, 372892266, 9959561867, 294465305959, 9551090908795, 337297690543923, 12886076807637021, 529624555043780909, 23305654066781507361, 1093356525580359412557
Offset: 0

Views

Author

Paul D. Hanna, Dec 25 2007

Keywords

Comments

P = A136220 is a triangular matrix where column k of P^3 equals column 0 of P^(3k+3) such that column 0 of P^3 equals column 0 of P shift one place left.

Crossrefs

Cf. A136220 (P), A136228 (U), A136236 (U^3); other columns of P: A136221, A136222, A136224.

Programs

  • PARI
    {a(n)=local(P=Mat(1),U,PShR);if(n==0,1,for(i=0,n+1, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#U,P[r,c], (U^c)[r-c+1,1]))));P[n+3,3])}

A136233 Matrix square of triangle U = A136228, read by rows.

Original entry on oeis.org

1, 2, 1, 10, 8, 1, 75, 76, 14, 1, 753, 888, 196, 20, 1, 9534, 12542, 3087, 370, 26, 1, 146353, 209506, 55552, 7320, 598, 32, 1, 2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1, 55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1
Offset: 0

Views

Author

Paul D. Hanna, Feb 07 2008

Keywords

Examples

			This triangle, U^2, begins:
1;
2, 1;
10, 8, 1;
75, 76, 14, 1;
753, 888, 196, 20, 1;
9534, 12542, 3087, 370, 26, 1;
146353, 209506, 55552, 7320, 598, 32, 1;
2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1;
55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1; ...
where column 0 of U^2 = column 1 of P = A136220.
		

Crossrefs

Cf. A136222 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136236 (U^3).

Programs

  • PARI
    {T(n,k)=local(P=Mat(1),U=Mat(1),PShR);if(n>0,for(i=0,n, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#R,P[r,c], (U^c)[r-c+1,1])))));(U^2)[n+1,k+1]}

Formula

Column k of U^2 (this triangle) = column 1 of P^(3k+1), where P = triangle A136220.
Showing 1-2 of 2 results.