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.

A121416 Matrix square of triangle A121412.

Original entry on oeis.org

1, 2, 1, 7, 2, 1, 43, 9, 2, 1, 403, 69, 11, 2, 1, 5188, 769, 101, 13, 2, 1, 85569, 11346, 1305, 139, 15, 2, 1, 1725291, 208914, 21745, 2043, 183, 17, 2, 1, 41145705, 4613976, 443329, 37971, 3015, 233, 19, 2, 1, 1133047596, 118840164, 10679494, 850260
Offset: 0

Views

Author

Paul D. Hanna, Aug 22 2006

Keywords

Comments

Row n of triangle T=A121412 equals row (n-1) of T^(n+1) with an appended '1'.

Examples

			Triangle begins:
1;
2, 1;
7, 2, 1;
43, 9, 2, 1;
403, 69, 11, 2, 1;
5188, 769, 101, 13, 2, 1;
85569, 11346, 1305, 139, 15, 2, 1;
1725291, 208914, 21745, 2043, 183, 17, 2, 1;
41145705, 4613976, 443329, 37971, 3015, 233, 19, 2, 1;
1133047596, 118840164, 10679494, 850260, 61860, 4253, 289, 21, 2, 1;

Crossrefs

Cf. A121412, A121420; A101479; columns: A121417, A121418, A121419.

Programs

  • PARI
    {T(n, k)=local(A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(A^i)[i-1, j]); )); A=B); return((A^2)[n+1, k+1])}

A121418 Column 0 of triangle A121416.

Original entry on oeis.org

1, 2, 7, 43, 403, 5188, 85569, 1725291, 41145705, 1133047596, 35377360292, 1234796503280, 47636225803285, 2012509471127885, 92398547122062997, 4580472438441602301, 243822925502110419105, 13870297863425823346284
Offset: 0

Views

Author

Paul D. Hanna, Aug 22 2006, Jan 19 2008

Keywords

Comments

Also column 1 of square array A136733.
A121416 is the matrix square of triangle A121412; row n of triangle T=A121412 equals row (n-1) of T^(n+1) with an appended '1'.

Crossrefs

Cf. A121416 (triangle); other columns: A121418, A121419.
Cf. A136733; A101483, A121421; A121425.

Programs

  • PARI
    {a(n)=local(A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i,j]=1, B[i, j]=(A^i)[i-1, j]); )); A=B); return((A^2)[n+1, 1])}

Extensions

Edited by N. J. A. Sloane, Oct 30 2008 at the suggestion of R. J. Mathar

A121417 Column 1 of triangle A121416.

Original entry on oeis.org

1, 2, 9, 69, 769, 11346, 208914, 4613976, 118840164, 3496297632, 115638728395, 4246267163601, 171369282105510, 7538270885559264, 358926669220446804, 18389706733665138450, 1008742283718489346668, 58981158542987625464424
Offset: 0

Views

Author

Paul D. Hanna, Aug 22 2006

Keywords

Comments

Also column 1 of square array A136737.
A121416 is the matrix square of triangle A121412; row n of triangle T=A121412 equals row (n-1) of T^(n+1) with an appended '1'.

Crossrefs

Cf. A121416 (triangle); other columns: A121418, A121419.
Cf. A136737; A121413, A121422; A121427, A136741.

Programs

  • PARI
    {a(n)=local(A=Mat(1), B); for(m=1, n+2, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i,j]=1, B[i, j]=(A^i)[i-1, j]); )); A=B); return((A^2)[n+2, 2])}

Extensions

Edited by N. J. A. Sloane, Oct 30 2008 at the suggestion of R. J. Mathar

A121428 Rectangular table, read by antidiagonals, where row n is equal to column 2 of matrix power A121412^(n+1) for n>=0.

Original entry on oeis.org

1, 1, 1, 1, 2, 5, 1, 3, 11, 45, 1, 4, 18, 101, 581, 1, 5, 26, 169, 1305, 9730, 1, 6, 35, 250, 2190, 21745, 199692, 1, 7, 45, 345, 3255, 36360, 443329, 4843125, 1, 8, 56, 455, 4520, 53916, 737051, 10679494, 135345925, 1, 9, 68, 581, 6006, 74781, 1087583, 17645187
Offset: 0

Views

Author

Paul D. Hanna, Aug 26 2006

Keywords

Examples

			Table of column 2 in matrix powers of triangle H=A121412 begins:
H^1: 1, 1, 5, 45, 581, 9730, 199692, 4843125, 135345925, ...
H^2: 1, 2, 11, 101, 1305, 21745, 443329, 10679494, 296547736, ...
H^3: 1, 3, 18, 169, 2190, 36360, 737051, 17645187, 487025244, ...
H^4: 1, 4, 26, 250, 3255, 53916, 1087583, 25889969, 710546530, ...
H^5: 1, 5, 35, 345, 4520, 74781, 1502270, 35578270, 971255050, ...
H^6: 1, 6, 45, 455, 6006, 99351, 1989113, 46890210, 1273698270, ...
H^7: 1, 7, 56, 581, 7735, 128051, 2556806, 60022670, 1622857887, ...
H^8: 1, 8, 68, 724, 9730, 161336, 3214774, 75190410, 2024181693, ...
H^9: 1, 9, 81, 885, 12015, 199692, 3973212, 92627235, 2483617140, ...
Rearrangement of the upper part of the table forms A121432, which is
the number of subpartitions of partition [0,0,0,1,1,1,1,2,2,2,2,2,..]:
1,1,1, 1,2,3,4, 5,11,18,26,35, 45,101,169,250,345,455, 581,1305,...

Crossrefs

Cf. A121429 (diagonal), A121431; rows: A121414, A121419, A121423; related tables: A121424, A121426; related triangles: A121412, A121416, A121420.

Programs

  • PARI
    {T(n,k)=local(H=Mat(1), B); for(m=1, k+3, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(H^i)[i-1, j]); )); H=B); return((H^(n+1))[k+3, 3])}
Showing 1-4 of 4 results.

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

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