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 1-4 of 4 results.

A113360 Matrix cube of triangle A113340.

Original entry on oeis.org

1, 3, 1, 12, 9, 1, 69, 81, 15, 1, 560, 879, 210, 21, 1, 6059, 11739, 3285, 399, 27, 1, 83215, 190044, 59395, 8127, 648, 33, 1, 1399161, 3654814, 1241270, 184436, 16245, 957, 39, 1, 28020221, 81947221, 29720808, 4695719, 442890, 28479, 1326, 45, 1
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Examples

			Triangle begins:
1;
3,1;
12,9,1;
69,81,15,1;
560,879,210,21,1;
6059,11739,3285,399,27,1;
83215,190044,59395,8127,648,33,1;
1399161,3654814,1241270,184436,16245,957,39,1;
28020221,81947221,29720808,4695719,442890,28479,1326,45,1; ...
		

Crossrefs

Cf. A113340, A113350, A113361 (column 1), A113362 (column 2), A113363 (column 3), A113364 (column 4); A113345 (A113340^2).

Programs

  • PARI
    T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^3)[n+1,k+1]

A113364 Column 4 of triangle A113360, also equals column 1 of A113360^3.

Original entry on oeis.org

1, 27, 648, 16245, 442890, 13269069, 437085705, 15779515035, 621549547326, 26584365342579, 1228849871633643, 61116983784901476, 3257058909552139683, 185287271910574343301, 11212875913429712533737, 719555515466643129103760
Offset: 0

Views

Author

Paul D. Hanna, Nov 09 2005

Keywords

Comments

A113360 equals the matrix cube of triangle A113340, where column 4 of A113340^3 = column 1 of A113340^9.

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113361 (column 1), A113362 (column 2), A113363 (column 3).

Programs

  • PARI
    a(n)=local(A,B); A=matrix(1,1);A[1,1]=1;for(m=2,n+5,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^3)[n+5,5]

A113362 Column 2 of triangle A113360, also equals column 1 of A113340^5.

Original entry on oeis.org

1, 15, 210, 3285, 59395, 1241270, 29720808, 806720492, 24568601477, 831697990069, 31036137984664, 1267376997249262, 56270606942915489, 2701018385881136958, 139463341982980040911, 7711492696761363573725
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113360 equals the matrix cube of triangle A113340, where column 2 of A113340^3 = column 1 of A113340^5.

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113361 (column 1), A113363 (column 3), A113364 (column 4).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+3,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^3)[n+3,3]

A113363 Column 3 of triangle A113360, also equals column 1 of A113340^7.

Original entry on oeis.org

1, 21, 399, 8127, 184436, 4695719, 133730310, 4234560596, 148077895854, 5680484146379, 237574859841676, 10771591113205720, 526750324271281348, 27655229128194306702, 1552379671658643163707, 92820542631741826797326
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113360 equals the matrix cube of triangle A113340, where column 3 of A113340^3 = column 1 of A113340^7.

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113361 (column 1), A113362 (column 2), A113364 (column 4).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+4,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^3)[n+4,4]
Showing 1-4 of 4 results.