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.

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A209975 Number of 2 X 2 matrices having all elements in {0,1,...,n} and determinant 3.

Original entry on oeis.org

0, 0, 1, 21, 29, 45, 65, 89, 105, 153, 169, 209, 249, 297, 321, 401, 433, 497, 545, 617, 649, 769, 809, 897, 977, 1057, 1105, 1249, 1297, 1409, 1489, 1609, 1673, 1873, 1937, 2033, 2129, 2273, 2345, 2585, 2649, 2809, 2929, 3097, 3177, 3369, 3457
Offset: 0

Views

Author

Clark Kimberling, Mar 16 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    (See the Mathematica section at A210000.)

A209976 Number of 2 X 2 matrices having all elements in {0,1,...,n} and determinant 4.

Original entry on oeis.org

0, 0, 5, 11, 43, 59, 83, 107, 155, 179, 227, 267, 331, 379, 451, 483, 579, 643, 715, 787, 915, 963, 1083, 1171, 1267, 1347, 1491, 1563, 1755, 1867, 1963, 2083, 2275, 2355, 2547, 2643, 2835, 2979, 3195, 3291, 3483, 3643, 3787, 3955, 4275, 4371
Offset: 0

Views

Author

Clark Kimberling, Mar 16 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    (See the Mathematica section at A210000.)

A209977 Number of 2 X 2 matrices having all elements in {0,1,...,n} and determinant 5.

Original entry on oeis.org

0, 0, 0, 3, 9, 45, 53, 77, 93, 117, 153, 193, 209, 257, 281, 353, 385, 449, 473, 545, 617, 665, 705, 793, 825, 985, 1033, 1105, 1153, 1265, 1337, 1457, 1521, 1601, 1665, 1881, 1929, 2073, 2145, 2241, 2385, 2545, 2593, 2761, 2841, 3057, 3145
Offset: 0

Views

Author

Clark Kimberling, Mar 16 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    (See the Mathematica section at A210000.)

A209980 (A197168)/2.

Original entry on oeis.org

0, 0, 1, 3, 9, 15, 25, 35, 49, 59, 81, 99, 113, 135, 169, 183, 213, 243, 277, 311, 341, 363, 421, 463, 493, 531, 601, 635, 681, 735, 781, 839, 901, 939, 1033, 1079, 1125, 1195, 1301, 1347, 1409, 1487, 1557, 1639, 1717, 1763, 1893, 1983, 2045, 2127
Offset: 0

Views

Author

Clark Kimberling, Mar 16 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    (See the Mathematica section at A209978.)

A209992 Number of 2 X 2 matrices with all elements in {1,2,...,n} and determinant in {0,1}.

Original entry on oeis.org

0, 1, 8, 23, 46, 77, 120, 167, 230, 301, 384, 463, 590, 685, 808, 959, 1118, 1245, 1448, 1591, 1830, 2053, 2256, 2431, 2766, 3005, 3248, 3535, 3886, 4109, 4560, 4799, 5182, 5549, 5872, 6295, 6870, 7157, 7520, 7959, 8582
Offset: 0

Views

Author

Clark Kimberling, Mar 18 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    a = 1; b = n; z1 = 40;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, 1}]
Table[c1[n, 1], {n, 0, z1}]   (* A209992 *)

A210283 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant n-1.

Original entry on oeis.org

0, 10, 7, 20, 29, 59, 53, 126, 91, 185, 172, 274, 179, 481, 245, 456, 492, 672, 383, 948, 479, 1097, 870, 1030, 669, 1864, 980, 1376, 1354, 2017, 1029, 2768, 1201, 2508, 1984, 2260, 2090, 4124, 1667, 2790, 2682, 4538, 2009, 5068, 2243, 4519
Offset: 0

Views

Author

Clark Kimberling, Mar 19 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n - 1], {n, 0, z1}]  (* A210283 *)

A210284 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant n+1.

Original entry on oeis.org

0, 0, 1, 11, 9, 42, 23, 81, 72, 126, 79, 273, 121, 268, 280, 416, 227, 624, 299, 761, 570, 690, 457, 1384, 672, 1004, 982, 1489, 769, 2108, 893, 1980, 1500, 1768, 1574, 3308, 1303, 2250, 2118, 3658, 1637, 4120, 1823, 3751, 3527, 3320
Offset: 0

Views

Author

Clark Kimberling, Mar 19 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n + 1], {n, 0, z1}]   (* A210284 *)

A210285 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant floor(n/2).

Original entry on oeis.org

1, 10, 7, 15, 36, 52, 65, 89, 155, 179, 153, 193, 374, 422, 287, 319, 617, 681, 584, 656, 914, 962, 639, 727, 1705, 1785, 889, 961, 1672, 1784, 1768, 1888, 2496, 2576, 1483, 1579, 3460, 3604, 1843, 1939, 4177, 4337, 3298, 3466, 3886, 3982
Offset: 0

Views

Author

Clark Kimberling, Mar 19 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, Floor[n/2]], {n, 0, z1}]   (* A210285 *)

A210290 Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative determinant.

Original entry on oeis.org

1, 13, 56, 160, 369, 733, 1328, 2216, 3505, 5285, 7680, 10792, 14809, 19813, 26024, 33600, 42721, 53549, 66384, 81336, 98761, 118821, 141784, 167888, 197561, 230917, 268352, 310176, 356753, 408285, 465376, 528088, 597049, 672533, 754944, 844744, 942425
Offset: 0

Views

Author

Clark Kimberling, Mar 19 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A059306, A210000.

Programs

  • Mathematica
    a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
Table[c1[n, n^2], {n, 0, z1}]   (* A210290 *)

Formula

a(n) = ((n+1)^4 + A059306(n))/2. - Andrew Howroyd, Apr 28 2020

Extensions

Terms a(34) and beyond from Andrew Howroyd, Apr 28 2020

A210291 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant >n.

Original entry on oeis.org

0, 0, 6, 40, 125, 323, 647, 1235, 2074, 3337, 5057, 7477, 10436, 14490, 19436, 25591, 33015, 42259, 52849, 65833, 80528, 97909, 117905, 141163, 166651, 196474, 229796, 267289, 308712, 355766, 406488, 464094, 526402, 595477, 670963
Offset: 0

Views

Author

Clark Kimberling, Mar 20 2012

Keywords

Comments

See A210000 for a guide to related sequences.

Links

Crossrefs

Cf. A210000.

Programs

  • Mathematica
    a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
Table[c1[n, n^2] - c1[n, n], {n, 0, z1}]  (* A210291 *)
Previous Showing 51-60 of 100 results. Next

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