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 16 results. Next

A183946 Number of strings of numbers x(i=1..n) in 0..2 with sum i^2*x(i) equal to n^2*2.

Original entry on oeis.org

1, 1, 2, 1, 5, 7, 10, 20, 37, 77, 118, 227, 385, 697, 1191, 2072, 3489, 5846, 9862, 16373, 26897, 44125, 71991, 116290, 187653, 300903, 478422, 761553, 1200692, 1893309, 2961406, 4630296, 7188253, 11155170, 17211745, 26490317, 40633554, 62126693
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2011

Keywords

Comments

Column 2 of A183953

Examples

			All solutions for n=4
..0
..0
..0
..2

Links

Programs

  • Mathematica
    r [n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[n, 2];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

A183947 Number of strings of numbers x(i=1..n) in 0..3 with sum i^2*x(i) equal to n^2*3.

Original entry on oeis.org

1, 1, 2, 4, 10, 26, 61, 147, 339, 771, 1721, 3770, 8123, 17233, 36041, 74322, 151368, 304614, 606305, 1194266, 2329462, 4501905, 8624652, 16386814, 30891283, 57801169, 107387377, 198165046, 363321016, 662012254, 1199130676, 2159720707
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2011

Keywords

Comments

Column 3 of A183953

Examples

			All solutions for n=4
..3....2....1....0
..1....3....1....0
..1....2....3....0
..2....1....1....3

Links

Programs

  • Mathematica
    r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[n, 3];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

A183954 Number of strings of numbers x(i=1..3) in 0..n with sum i^2*x(i) equal to n*9.

Original entry on oeis.org

1, 2, 2, 3, 4, 6, 7, 9, 12, 14, 17, 19, 22, 25, 29, 32, 36, 41, 45, 50, 54, 59, 64, 70, 75, 81, 88, 94, 101, 107, 114, 121, 129, 136, 144, 153, 161, 170, 178, 187, 196, 206, 215, 225, 236, 246, 257, 267, 278, 289, 301, 312, 324, 337, 349, 362, 374, 387, 400, 414, 427, 441
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2011

Keywords

Comments

Row 3 of A183953.

Examples

			All solutions for n=3:
..0....1
..0....2
..3....2

Links

Crossrefs

Cf. A183953.

Programs

  • Mathematica
    r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[3, n];
Table[a[n], {n, 1, 62}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11).
Empirical g.f.: x*(1 + x)*(1 - x + x^3 - x^4 + 2*x^5 - 3*x^6 + 4*x^7 - 3*x^8 + x^9) / ((1 - x)^3*(1 + x + x^2)*(1 + x^3 + x^6)). - Colin Barker, Apr 07 2018

A183955 Number of strings of numbers x(i=1..4) in 0..n with sum i^2*x(i) equal to n*16.

Original entry on oeis.org

1, 1, 4, 8, 14, 21, 32, 48, 61, 82, 108, 139, 172, 210, 256, 311, 365, 427, 500, 582, 666, 759, 864, 982, 1097, 1228, 1372, 1529, 1688, 1860, 2048, 2253, 2457, 2677, 2916, 3172, 3430, 3705, 4000, 4316, 4629, 4966, 5324, 5703, 6084, 6486, 6912, 7363, 7813, 8287
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2011

Keywords

Comments

Row 4 of A183953.

Examples

			All solutions for n=3:
..2....3....0....1
..3....1....0....1
..2....1....0....3
..1....2....3....1

Links

Crossrefs

Cf. A183953.

Programs

  • Mathematica
    r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[4, n];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) + a(n-16) - 2*a(n-17) + a(n-18) - a(n-20) + 2*a(n-21)-a(n-22).
Empirical g.f.: x*(1 - x + 3*x^2 + x^3 + x^4 + 2*x^5 + x^6 + 4*x^7 - 5*x^8 + 7*x^9 + x^10 + 5*x^12 - 3*x^13 + 3*x^14 + 4*x^15 - 4*x^16 + 4*x^17 - x^19 + 2*x^20 - x^21) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2*(1 + x^4)*(1 + x^8)). - Colin Barker, Apr 07 2018

A183945 Number of strings of numbers x(i=1..n) in 0..n with sum i^2*x(i) equal to n^3.

Original entry on oeis.org

1, 1, 2, 8, 53, 398, 3539, 34847, 369777, 4178324, 49657281, 615829513, 7919376470, 105084836323, 1433178519184, 20025465352373, 285916536136122, 4162074154247193, 61656883471361641, 928025931557339662
Offset: 1

Views

Author

R. H. Hardin Jan 08 2011

Keywords

Comments

Diagonal of A183953

Examples

			All solutions for n=4
..0....2....4....1....0....3....4....0
..3....3....2....1....0....1....3....4
..4....2....4....3....0....1....0....0
..1....2....1....2....4....3....3....3

Links

A183948 Number of strings of numbers x(i=1..n) in 0..4 with sum i^2*x(i) equal to n^2*4.

Original entry on oeis.org

1, 2, 3, 8, 27, 78, 219, 649, 1805, 4987, 13179, 34331, 87203, 217281, 532073, 1278041, 3025466, 7046194, 16192534, 36706373, 82197783, 181900279, 398099637, 862217855, 1848842707, 3927404946, 8267742253, 17257223344, 35726693834
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2011

Keywords

Comments

Column 4 of A183953

Examples

			Some solutions for n=6
..0....4....2....3....4....0....3....2....2....0....4....0....2....3....4....2
..2....1....2....3....4....3....0....1....4....2....1....3....1....4....1....1
..2....2....1....2....3....0....1....0....2....1....1....1....1....0....4....4
..2....2....4....0....0....2....2....1....0....1....1....3....2....4....4....1
..2....2....1....3....1....4....4....2....0....3....3....3....1....1....0....2
..1....1....1....1....2....0....0....2....3....1....1....0....2....1....1....1

Links

Programs

  • Mathematica
    r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[n, 4];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

A183949 Number of strings of numbers x(i=1..n) in 0..5 with sum i^2*x(i) equal to n^2*5.

Original entry on oeis.org

1, 2, 4, 14, 53, 180, 656, 2195, 7250, 23044, 71123, 213368, 624425, 1784399, 4986210, 13657266, 36691985, 96863639, 251472815, 642811767, 1619203005, 4022796235, 9864987052, 23894800443, 57205375668, 135438579331, 317296680619
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2011

Keywords

Comments

Column 5 of A183953

Examples

			All solutions for n=4
..0....1....0....3....3....3....4....2....4....1....5....0....3....5
..3....1....4....0....1....4....3....3....2....5....4....0....5....0
..4....3....0....5....1....5....0....2....4....3....3....0....1....3
..2....3....4....2....4....1....4....3....2....2....2....5....3....3

Links

Programs

  • Mathematica
    r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[n, 5];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

A183950 Number of strings of numbers x(i=1..n) in 0..6 with sum i^2*x(i) equal to n^2*6.

Original entry on oeis.org

1, 2, 6, 21, 94, 398, 1613, 6301, 23611, 85595, 299789, 1018889, 3364983, 10823939, 33973701, 104224215, 313017236, 921527638, 2662917595, 7561290034, 21119173722, 58077373552, 157382658382, 420599245799, 1109306162737
Offset: 1

Views

Author

R. H. Hardin Jan 08 2011

Keywords

Comments

Column 6 of A183953

Examples

			Some solutions for n=4
..3....0....2....6....5....6....6....0....0....1....2....4....1....3....4....5
..1....3....3....1....0....6....5....4....0....5....6....2....1....4....6....4
..1....4....2....6....3....2....6....0....0....3....6....4....3....5....4....3
..5....3....4....2....4....3....1....5....6....3....1....3....4....2....2....3

Links

A183951 Number of strings of numbers x(i=1..n) in 0..7 with sum i^2*x(i) equal to n^2*7.

Original entry on oeis.org

1, 2, 7, 32, 161, 770, 3539, 15601, 65909, 268008, 1051270, 3988203, 14668943, 52424801, 182419618, 619151665, 2053195642, 6662236128, 21181322973, 66063536142, 202362531609, 609394911084, 1805804155160, 5270044397919
Offset: 1

Views

Author

R. H. Hardin Jan 08 2011

Keywords

Comments

Column 7 of A183953

Examples

			Some solutions for n=4
..7....5....4....7....3....3....1....2....1....2....6....5....3....6....5....0
..3....7....7....4....0....5....4....7....5....6....1....4....1....2....0....4
..5....7....0....1....5....1....7....2....3....6....6....3....1....2....3....0
..3....1....5....5....4....5....2....4....4....2....3....4....6....5....5....6

Links

A183952 Number of strings of numbers x(i=1..n) in 0..8 with sum i^2*x(i) equal to n^2*8.

Original entry on oeis.org

1, 3, 9, 48, 259, 1387, 7099, 34847, 163588, 737538, 3200055, 13400036, 54289217, 213301597, 814463579, 3028171125, 10981909481, 38908787433, 134868584027, 457962911722, 1525173224446, 4987066348804, 16026405323579, 50662230359800
Offset: 1

Views

Author

R. H. Hardin Jan 08 2011

Keywords

Comments

Column 8 of A183953

Examples

			Some solutions for n=4
..1....7....5....0....3....4....4....0....1....2....8....2....8....3....4....8
..1....8....7....2....5....1....7....0....0....2....6....3....4....1....2....8
..3....1....7....8....1....8....0....0....7....6....0....2....8....1....4....8
..6....5....2....3....6....3....6....8....4....4....6....6....2....7....5....1

Links

Showing 1-10 of 16 results. Next

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

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