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.

Previous Showing 21-28 of 28 results.

A113357 Column 1 of triangle A113355, also equals column 0 of A113355^2.

Original entry on oeis.org

1, 8, 68, 712, 9270, 147174, 2786270, 61662544, 1568627031, 45226595865, 1460494997316, 52298603045920, 2059014449303471, 88476000281671109, 4123177399591735062, 207239886694280045429, 11179817701706220363653
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113355 equals the matrix square of A113350, where column 1 of A113350^2 = column 0 of A113350^4.

Crossrefs

Cf. A113340, A113350, A113355, A113356 (column 0), A113358 (column 2), A113359 (column 3).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+2,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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+2,2]

A113358 Column 2 of triangle A113355, also equals column 0 of A113355^3.

Original entry on oeis.org

1, 12, 150, 2184, 37523, 754171, 17502145, 462930509, 13792292332, 458112945183, 16812390472566, 676432435584855, 29635374525536866, 1405425902409792025, 71770681806834337871, 3928431507732054301085, 229528875492540329214765
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113355 equals the matrix square of A113350, where column 2 of A113350^2 = column 0 of A113350^6.

Crossrefs

Cf. A113340, A113350, A113355, A113356 (column 0), A113357 (column 1), A113359 (column 3).

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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+3,3]

A113359 Column 3 of triangle A113355, also equals column 0 of A113355^4.

Original entry on oeis.org

1, 16, 264, 4912, 104476, 2531004, 69265724, 2122120824, 72160283026, 2702008172582, 110631977612048, 4922281897250776, 236665779016591350, 12236187035970192634, 677311496213007409312, 39980910968200568816168
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113355 equals the matrix square of A113350, where column 3 of A113350^2 = column 0 of A113350^8.

Crossrefs

Cf. A113340, A113350, A113355, A113356 (column 0), A113357 (column 1), A113358 (column 2).

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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+4,4]

A113361 Column 1 of triangle A113360, which equals the matrix cube of triangle A113340.

Original entry on oeis.org

1, 9, 81, 879, 11739, 190044, 3654814, 81947221, 2107962168, 61366149296, 1998607800064, 72112467306074, 2858551691428042, 123596917897265255, 5792708223233376744, 292682081981049699408, 15865848522184194142469
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113362 (column 2), 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+2,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+2,2]

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]

A113366 Column 1 of triangle A113365, also equals column 1 of A113340^4.

Original entry on oeis.org

1, 12, 138, 1830, 28805, 535004, 11568197, 287143993, 8077888153, 254672147047, 8910929460415, 343135184110984, 14435616939387951, 659276261774240232, 32504007393860850275, 1721495715845423489806, 97516667477625085469176
Offset: 0

Views

Author

Paul D. Hanna, Nov 09 2005

Keywords

Comments

A113365 equals the matrix cube of A113350, where column 1 of A113350^3 = column 1 of A113340^4.

Crossrefs

Cf. A113340, A113350, A113365 (=A113350^3), A113346 (column 0), A113367 (column 2); A113355 (=A113350^2), A113360 (=A113340^3).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+2,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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^3)[n+2,2]

A113367 Column 2 of triangle A113365, also equals column 1 of A113340^6.

Original entry on oeis.org

1, 18, 297, 5349, 109095, 2529909, 66345668, 1951815218, 63879120597, 2307569048308, 91351738972187, 3937843359099176, 183778364128820499, 9238674078250458082, 497996763423626058847, 28666454637876852704364
Offset: 0

Views

Author

Paul D. Hanna, Nov 09 2005

Keywords

Comments

A113365 equals the matrix cube of A113350, where column 2 of A113350^3 = column 1 of A113340^6.

Crossrefs

Cf. A113340, A113350, A113365 (=A113350^3), A113346 (column 0), A113366 (column 1).

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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^3)[n+3,3]
Previous Showing 21-28 of 28 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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