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.

User: Álvar Ibeas

Álvar Ibeas's wiki page.

Álvar Ibeas has authored 61 sequences. Here are the ten most recent ones:

A348181 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_5)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 5, 59, 2360, 369540, 258838575
Offset: 1

Views

Author

Álvar Ibeas, Oct 05 2021

Keywords

Crossrefs

Cf. A348180, A036038, A347843, A348116-A348118.

Formula

a(n) = Sum_{L partition of n} A348180(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

A348180 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_5)^n, counted up to coordinate permutation, with dimension increments given by (any fixed permutation of) the parts of the k-th partition of n in Abramowitz-Stegun order.

Original entry on oeis.org

1, 1, 4, 1, 9, 40, 1, 19, 56, 279, 1428, 1, 33, 289, 1561, 6345, 35689, 202421, 1, 55, 1358, 4836, 7652, 129505, 615395, 757560, 3620918, 21341449, 125952538, 1, 85, 5771, 80605, 33435, 2362185, 10691648, 53822709, 14039541, 321134138, 1622410155, 1916573757, 9688635876, 57866763847
Offset: 1

Views

Author

Álvar Ibeas, Oct 05 2021

Keywords

Comments

A permutation on the list of dimension increments does not modify the number of subspace chains.
The length of the enumerated chains is r = len(L), where L is the parameter partition.

Examples

			For L = (1, 1, 1), there are 186 (= 31 * 6) = A347488(3, 3) subspace chains 0 < V_1 < V_2 < (F_5)^3.
The permutations of the three coordinates classify them into 40 = T(3, 3) orbits.
T(3, 2) = 9 refers to partition (2, 1) and counts subspace chains in (F_5)^2 with dimensions (0, 2, 3), i.e. 2-dimensional subspaces. It also counts chains with dimensions (0, 1, 3), i.e. 1-dimensional subspaces.
Triangle begins:
  k:  1  2   3    4    5     6      7
      -------------------------------
n=1:  1
n=2:  1  4
n=3:  1  9  40
n=4:  1 19  56  279 1428
n=5:  1 33 289 1561 6345 35689 202421

Links

Crossrefs

Cf. A347972, A347488, A348113-A348115.

Formula

If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A347972(n, a) = A347972(n, n-a).

A348118 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_4)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 4, 39, 876, 60117, 14466888
Offset: 1

Views

Author

Álvar Ibeas, Oct 01 2021

Keywords

Crossrefs

Cf. A348115, A036038, A347842.

Formula

a(n) = Sum_{L partition of n} A348115(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

A348117 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_3)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 4, 26, 334, 8474, 511198, 81719819
Offset: 1

Views

Author

Álvar Ibeas, Oct 01 2021

Keywords

Crossrefs

Cf. A348114, A036038, A347841.

Formula

a(n) = Sum_{L partition of n} A348114(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

A348116 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_2)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 3, 13, 82, 747, 10248, 217703, 7530572, 447825441
Offset: 1

Views

Author

Álvar Ibeas, Oct 01 2021

Keywords

Crossrefs

Cf. A348113, A036038, A289545.

Formula

a(n) = Sum_{L partition of n} A348113(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

A348115 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_4)^n, counted up to coordinate permutation, with dimension increments given by (any fixed permutation of) the parts of the k-th partition of n in Abramowitz-Stegun order.

Original entry on oeis.org

1, 1, 3, 1, 7, 24, 1, 12, 31, 117, 469, 1, 19, 111, 458, 1435, 6356, 28753, 1, 29, 361, 964, 1579, 15266, 55470, 71660, 264300, 1267174, 6105030, 1, 41, 1068, 8042, 4886, 145628, 494779, 1952843, 705790, 9589197, 38323695, 47157299, 188963325, 932529235
Offset: 1

Views

Author

Álvar Ibeas, Oct 01 2021

Keywords

Comments

A permutation on the list of dimension increments does not modify the number of subspace chains.
The length of the enumerated chains is r = len(L), where L is the parameter partition.

Examples

			For L = (1, 1, 1), there are 105 (= 21 * 5) = A347487(3, 3) subspace chains 0 < V_1 < V_2 < (F_4)^3.
The permutations of the three coordinates classify them into 24 = T(3, 3) orbits.
T(3, 2) = 7 refers to partition (2, 1) and counts subspace chains in (F_4)^2 with dimensions (0, 2, 3), i.e., 2-dimensional subspaces. It also counts chains with dimensions (0, 1, 3), i.e., 1-dimensional subspaces.
Triangle begins:
  k:  1  2   3   4    5    6     7
      ----------------------------
n=1:  1
n=2:  1  3
n=3:  1  7  24
n=4:  1 12  31 117  469
n=5:  1 19 111 458 1435 6356 28753

Links

Crossrefs

Cf. A347971, A347487.

Formula

If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A347971(n, a) = A347971(n, n-a).

A348114 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_3)^n, counted up to coordinate permutation, with dimension increments given by (any fixed permutation of) the parts of the k-th partition of n in Abramowitz-Stegun order.

Original entry on oeis.org

1, 1, 3, 1, 5, 15, 1, 8, 16, 49, 154, 1, 11, 39, 126, 288, 964, 3275, 1, 15, 87, 168, 291, 1412, 3600, 4957, 12865, 46400, 168862, 1, 19, 176, 644, 608, 6101, 14001, 38996, 22294, 146064, 418072, 549894, 1586761, 6045724, 23115063, 1, 24, 338, 2348, 4849, 1195, 24329
Offset: 1

Views

Author

Álvar Ibeas, Oct 01 2021

Keywords

Comments

A permutation on the list of dimension increments does not modify the number of subspace chains.
The length of the enumerated chains is r = len(L), where L is the parameter partition.

Examples

			For L = (1, 1, 1), there are 52 (= 13 * 4) = A347486(3, 3) subspace chains 0 < V_1 < V_2 < (F_3)^3.
The permutations of the three coordinates classify them into 15 = T(3, 3) orbits.
T(3, 2) = 5 refers to partition (2, 1) and counts subspace chains in (F_3)^2 with dimensions (0, 2, 3), i.e. 2-dimensional subspaces. It also counts chains with dimensions (0, 1, 3), i.e. 1-dimensional subspaces.
Triangle begins:
  k:  1  2  3   4   5   6    7
      ------------------------
n=1:  1
n=2:  1  3
n=3:  1  5 15
n=4:  1  8 16  49 154
n=5:  1 11 39 126 288 964 3275

Links

Crossrefs

Cf. A347970, A347486.

Formula

If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A347970(n, a) = A347970(n, n-a).

A348113 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_2)^n, counted up to coordinate permutation, with dimension increments given by (any fixed permutation of) the parts of the k-th partition of n in Abramowitz-Stegun order.

Original entry on oeis.org

1, 1, 2, 1, 3, 6, 1, 4, 6, 13, 28, 1, 5, 10, 23, 37, 85, 196, 1, 6, 16, 22, 37, 87, 149, 207, 357, 864, 2109, 1, 7, 23, 43, 55, 180, 269, 479, 441, 1193, 2169, 2992, 5483, 13958, 35773, 1, 8, 32, 77, 106, 78, 341, 734, 1354, 2153, 856, 3468, 5559, 10544, 20185, 8943, 27572, 53115, 72517, 140563, 373927
Offset: 1

Views

Author

Álvar Ibeas, Oct 01 2021

Keywords

Comments

A permutation on the list of dimension increments does not modify the number of subspace chains.
The length of the enumerated chains is r = len(L), where L is the parameter partition.

Examples

			For L = (1, 1, 1), there are 21 (= 7 * 3) = A347485(3, 3) subspace chains 0 < V_1 < V_2 < (F_2)^3.
The permutations of the three coordinates classify them into 6 = T(3, 3) orbits:
<e_1>, <e_1, e_2>;                     <e_1>, <e_1, e_2 + e_3>;
<e_1 + e_2>, <e_1, e_2>;               <e_1 + e_2>, <e_1 + e_2, e_3>;
<e_1 + e_2>, <e_1 + e_2, e_1 + e_3>;   <e_1 + e_2 + e_3>, <e_1 + e_2, e_3>.
T(3, 2) = 3 refers to partition (2, 1) and counts subspace chains in (F_2)^2 with dimensions (0, 2, 3), i.e., 2-dimensional subspaces. It also counts chains with dimensions (0, 1, 3), i.e., 1-dimensional subspaces.
Triangle begins:
  k:  1 2  3  4  5  6   7   8   9  10   11
      ------------------------------------
n=1:  1
n=2:  1 2
n=3:  1 3  6
n=4:  1 4  6 13 28
n=5:  1 5 10 23 37 85 196
n=6:  1 6 16 22 37 87 149 207 357 864 2109

Links

Crossrefs

Cf. A076831, A347485.

Formula

If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A076831(n, a) = A076831(n, n-a).

A348107 a(n) is the number of vector subspaces in (F_9)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 2, 8, 44, 504, 12128, 810616, 134312136, 65039805696, 77906886854938
Offset: 0

Views

Author

Álvar Ibeas, Sep 30 2021

Keywords

Crossrefs

Row sums of A347975. Cf. A015195.

A348106 a(n) is the number of vector subspaces in (F_8)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 2, 7, 36, 338, 6370, 301736, 34015760, 10395343595, 7592404159342
Offset: 0

Views

Author

Álvar Ibeas, Sep 30 2021

Keywords

Crossrefs

Row sums of A347974. Cf. A006122.

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

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