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 1-10 of 11 results. Next

A185628 Triangle, read by rows, equal to the matrix cube of triangle A185620.

Original entry on oeis.org

1, 3, 1, 6, 3, 1, 16, 12, 3, 1, 60, 55, 18, 3, 1, 305, 315, 118, 24, 3, 1, 1988, 2243, 912, 205, 30, 3, 1, 15951, 19378, 8342, 1995, 316, 36, 3, 1, 153171, 198363, 89193, 22274, 3708, 451, 42, 3, 1, 1722693, 2358860, 1098552, 283427, 48863, 6195, 610, 48, 3, 1, 22296396, 32060736
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Examples

			 Triangle begins:
1;
3, 1;
6, 3, 1;
16, 12, 3, 1;
60, 55, 18, 3, 1;
305, 315, 118, 24, 3, 1;
1988, 2243, 912, 205, 30, 3, 1;
15951, 19378, 8342, 1995, 316, 36, 3, 1;
153171, 198363, 89193, 22274, 3708, 451, 42, 3, 1;
1722693, 2358860, 1098552, 283427, 48863, 6195, 610, 48, 3, 1;
22296396, 32060736, 15376126, 4070883, 720586, 94085, 9600, 793, 54, 3, 1; ...
This triangle equals the matrix cube, R^3, of triangle R = A185620, which begins:
1;
1, 1;
1, 1, 1;
1, 3, 1, 1;
1, 10, 5, 1, 1;
1, 42, 27, 7, 1, 1;
1, 226, 173, 52, 9, 1, 1;
1, 1525, 1330, 442, 85, 11, 1, 1;
1, 12555, 12134, 4345, 897, 126, 13, 1, 1; ...
where R^3 - R^2 + I equals R shifted left one column.

Crossrefs

Cf. A185620, A185624, A185629, A185630, A185631.

A185624 Triangle, read by rows, equal to the matrix square of triangle A185620.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 6, 7, 2, 1, 18, 28, 11, 2, 1, 79, 142, 66, 15, 2, 1, 463, 913, 470, 120, 19, 2, 1, 3396, 7244, 3997, 1098, 190, 23, 2, 1, 30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1, 314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1, 3796561, 9933242, 6208551, 1921122
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Examples

			 Triangle begins:
1;
2, 1;
3, 2, 1;
6, 7, 2, 1;
18, 28, 11, 2, 1;
79, 142, 66, 15, 2, 1;
463, 913, 470, 120, 19, 2, 1;
3396, 7244, 3997, 1098, 190, 23, 2, 1;
30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1;
314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1;
3796561, 9933242, 6208551, 1921122, 377495, 53149, 5742, 496, 35, 2, 1; ...
This triangle equals the matrix square, R^2, of triangle R = A185620, which begins:
1;
1, 1;
1, 1, 1;
1, 3, 1, 1;
1, 10, 5, 1, 1;
1, 42, 27, 7, 1, 1;
1, 226, 173, 52, 9, 1, 1;
1, 1525, 1330, 442, 85, 11, 1, 1;
1, 12555, 12134, 4345, 897, 126, 13, 1, 1; ...
where R^3 - R^2 + I equals R shifted left one column.

Crossrefs

Cf. A185620, A185625, A185626, A185627, A185628.

A185621 Column 1 of triangular matrix T = A185620, which satisfies: T^3 - T^2 + I = SHIFT_LEFT(T).

Original entry on oeis.org

1, 1, 3, 10, 42, 226, 1525, 12555, 123098, 1408656, 18499835, 274937571, 4569703790, 84104161618, 1699644180677, 37442806230267, 893577983768401, 22976420374082264, 633487846228307145, 18649221873212499505
Offset: 0

Views

Author

Paul D. Hanna, Feb 01 2011

Keywords

Crossrefs

Cf. A185620, A185622, A185623.

A185622 Column 2 of triangular matrix T = A185620, which satisfies: T^3 - T^2 + I = SHIFT_LEFT(T).

Original entry on oeis.org

1, 1, 5, 27, 173, 1330, 12134, 129359, 1587501, 22127494, 346245249, 6021401618, 115373290404, 2417393483696, 55028734386699, 1353170738090204, 35764709876549353, 1011496211524329699, 30490289594142366215
Offset: 0

Views

Author

Paul D. Hanna, Feb 01 2011

Keywords

Crossrefs

Cf. A185620, A185621, A185623.

A185623 Column 3 of triangular matrix T = A185620, which satisfies: T^3 - T^2 + I = SHIFT_LEFT(T).

Original entry on oeis.org

1, 1, 7, 52, 442, 4345, 49114, 632104, 9167575, 148388893, 2657338636, 52244218837, 1120000171417, 26024217218746, 651943279016898, 17525338687574976, 503409841260165202, 15393623230236299133
Offset: 0

Views

Author

Paul D. Hanna, Feb 01 2011

Keywords

Crossrefs

Cf. A185620, A185621, A185622.

A185625 Column 0 of triangle A185624; also, equals row sums of triangle A185620.

Original entry on oeis.org

1, 2, 3, 6, 18, 79, 463, 3396, 30073, 314037, 3796561, 52332869, 812013163, 14029926801, 267461387125, 5581705418715, 126657160962835, 3106644875467396, 81943115662983569, 2313753122033185373, 69654973411269008826, 2227679407193350385775
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Comments

Triangle A185624 equals the matrix square of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

Crossrefs

Cf. A185620, A185624, A185626, A185627, A185628.

A185626 Column 1 of triangle A185624.

Original entry on oeis.org

1, 2, 7, 28, 142, 913, 7244, 69004, 771359, 9933242, 145148660, 2376879719, 43167728519, 861914166441, 18779307089740, 443624137266205, 11299168270825627, 308780443524256478, 9014690419440269085, 280081388252523565158, 9229143937723290061482
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Comments

Triangle A185624 equals the matrix square of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

Crossrefs

Cf. A185620, A185624, A185625, A185627, A185628.

A185627 Column 2 of triangle A185624.

Original entry on oeis.org

1, 2, 11, 66, 470, 3997, 40079, 466448, 6208551, 93297013, 1565360082, 29047075343, 591275224311, 13110484254998, 314726620750589, 8135993235767295, 225426087495479680, 6666553071325468948, 209645759506867904384, 6987310422457948266944, 246075579251657940919613
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Comments

Triangle A185624 equals the matrix square of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

Crossrefs

Cf. A185620, A185624, A185625, A185626, A185628.

A185629 Column 0 of triangle A185628; also, equals row sums of triangle A185624.

Original entry on oeis.org

1, 3, 6, 16, 60, 305, 1988, 15951, 153171, 1722693, 22296396, 327270440, 5381716953, 98134088419, 1967105567802, 43024511648982, 1020235144731236, 26083065249549660, 715430961891290714, 20962974995245684878, 653654392800091507791, 21615444263990028093227
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Comments

Triangle A185628 equals the matrix cube of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

Crossrefs

Cf. A185620, A185628, A185630, A185631.

Programs

  • PARI
    {a(n)=local(A=Mat(1), B); for(m=1, n+1, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^3)[n+1, 1])}

A185630 Column 1 of triangle A185628.

Original entry on oeis.org

1, 3, 12, 55, 315, 2243, 19378, 198363, 2358860, 32060736, 491393909, 8398281337, 158541018923, 3279307650137, 73808041476439, 1796794875356409, 47063878147374980, 1320276655048586177, 39504980013582635300, 1256210676237601811305, 42313074100060933324771
Offset: 0

Views

Author

Paul D. Hanna, Sep 07 2011

Keywords

Comments

Triangle A185628 equals the matrix cube of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

Crossrefs

Cf. A185620, A185628, A185629, A185631.

Programs

  • PARI
    {a(n)=local(A=Mat(1), B); for(m=1, n+2, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^3)[n+2, 2])}
Showing 1-10 of 11 results. Next

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

Content is available under The OEIS End-User License Agreement.