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

A184695 Number of strings of numbers x(i=1..n) in 0..n with sum i*x(i) equal to n^2.

Original entry on oeis.org

1, 2, 6, 28, 156, 985, 6575, 46037, 332729, 2467215, 18668476, 143639875, 1120736308, 8848906376, 70585065382, 568063412434, 4607556545105, 37630962749979, 309239715248494, 2555320702164649, 21220771891605441
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Diagonal of A184703

Examples

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

Links

A184696 Number of strings of numbers x(i=1..n) in 0..2 with sum i*x(i) equal to n*2.

Original entry on oeis.org

1, 2, 3, 7, 12, 21, 35, 58, 91, 142, 215, 322, 472, 685, 979, 1385, 1936, 2684, 3685, 5023, 6790, 9119, 12163, 16130, 21264, 27887, 36383, 47249, 61076, 78621, 100787, 128714, 163766, 207643, 262385, 330506, 415023, 519630, 648751, 807768, 1003113, 1242574
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Column 2 of A184703

Examples

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

Links

A184697 Number of strings of numbers x(i=1..n) in 0..3 with sum i*x(i) equal to n*3.

Original entry on oeis.org

1, 2, 6, 14, 34, 74, 154, 304, 580, 1066, 1901, 3304, 5610, 9332, 15241, 24476, 38721, 60418, 93088, 141765, 213590, 318608, 470873, 689907, 1002660, 1446141, 2070897, 2945590, 4163079, 5848345, 8168863, 11348145, 15683285, 21567664, 29520301
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Column 3 of A184703

Examples

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

Links

A184698 Number of strings of numbers x(i=1..n) in 0..4 with sum i*x(i) equal to n*4.

Original entry on oeis.org

1, 3, 9, 28, 78, 207, 504, 1169, 2574, 5439, 11071, 21841, 41846, 78193, 142787, 255441, 448444, 773966, 1314861, 2201731, 3637642, 5935817, 9574284, 15277075, 24130784, 37755124, 58545388, 90021407, 137320211, 207895383, 312495662
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Column 4 of A184703

Examples

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

Links

A184699 Number of strings of numbers x(i=1..n) in 0..5 with sum i*x(i) equal to n*5.

Original entry on oeis.org

1, 3, 12, 46, 156, 476, 1349, 3571, 8939, 21310, 48701, 107233, 228465, 472626, 952169, 1872813, 3604103, 6798753, 12592030, 22930495, 41108069, 72630552, 126596216, 217879554, 370555433, 623223294, 1037221437, 1709205913
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Column 5 of A184703

Examples

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

Links

A184700 Number of strings of numbers x(i=1..n) in 0..6 with sum i*x(i) equal to n*6.

Original entry on oeis.org

1, 4, 17, 74, 282, 985, 3142, 9353, 26146, 69331, 175410, 426006, 997336, 2259816, 4971190, 10646876, 22251915, 45477519, 91049794, 178855119, 345194427, 655396606, 1225461491, 2258813924, 4108018840, 7377439511, 13092332036
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Column 6 of A184703

Examples

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

Links

A184701 Number of strings of numbers x(i=1..n) in 0..7 with sum i*x(i) equal to n*7.

Original entry on oeis.org

1, 4, 22, 107, 471, 1842, 6575, 21713, 67105, 195760, 543050, 1440869, 3674381, 9042422, 21548644, 49872800, 112387351, 247136196, 531320447, 1118701390, 2310261518, 4685733808, 9345070552, 18346037917, 35487652677, 67696833402
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2011

Keywords

Comments

Column 7 of A184703.

Examples

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

Links

Crossrefs

Cf. A184703.

Programs

  • Maple
    F:= proc(n,t) option remember; local d,s;
  if n = 1 then return `if`(t<=7,1,0) fi;
  s:= 0:
  for d from 0 to min(7, t/n) do
    s:= s + procname(n-1,t-n*d)
  od:
  s
end proc:
seq(F(n,7*n),n=1..100); # Robert Israel, Feb 13 2017
  • Mathematica
    F[n_, t_] := F[n, t] = Module[{d, s}, If[n == 1, Return[If[t <= 7, 1, 0]]]; s = 0; For[d = 0, d <= Min[7, t/n], d++, s += F[n - 1, t - n*d]]; s];
Table[F[n, 7*n], {n, 1, 100}] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)

A184702 Number of strings of numbers x(i=1..n) in 0..8 with sum i*x(i) equal to n*8.

Original entry on oeis.org

1, 5, 27, 154, 744, 3226, 12688, 46037, 155645, 495251, 1493647, 4296714, 11848026, 31451899, 80666519, 200509690, 484315994, 1139426161, 2616322539, 5873891912, 12914638982, 27846986092, 58961254653, 122728579066, 251399638554
Offset: 1

Views

Author

R. H. Hardin Jan 20 2011

Keywords

Comments

Column 8 of A184703

Examples

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

Links

A184704 Number of strings of numbers x(i=1..4) in 0..n with sum i*x(i) equal to n*4.

Original entry on oeis.org

2, 7, 14, 28, 46, 74, 107, 154, 208, 278, 357, 456, 565, 697, 841, 1011, 1195, 1408, 1636, 1897, 2175, 2488, 2820, 3191, 3582, 4015, 4470, 4970, 5494, 6066, 6663, 7312, 7988, 8718, 9477, 10294, 11141, 12049, 12989, 13993, 15031, 16136, 17276, 18487, 19735
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2011

Keywords

Comments

Row 4 of A184703.

Examples

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

Links

Crossrefs

Cf. A184703.

Formula

Empirical: a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).
Empirical g.f.: x*(2 + 5*x + 5*x^2 + 7*x^3 + 4*x^4 + 4*x^5 + x^6 + x^7 + x^8 - x^9) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Apr 14 2018

A184705 Number of strings of numbers x(i=1..5) in 0..n with sum i*x(i) equal to n*5.

Original entry on oeis.org

3, 12, 34, 78, 156, 282, 471, 744, 1119, 1623, 2279, 3118, 4167, 5463, 7039, 8935, 11188, 13845, 16946, 20545, 24685, 29424, 34812, 40911, 47775, 55472, 64060, 73612, 84190, 95874, 108729, 122840, 138277, 155129, 173473, 193402, 214995, 238353
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2011

Keywords

Comments

Row 5 of A184703.

Examples

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

Links

Crossrefs

Cf. A184703.

Formula

Empirical: a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-9) + a(n-10) - a(n-13) - a(n-14) + a(n-15).
Empirical g.f.: x*(3 + 9*x + 19*x^2 + 32*x^3 + 44*x^4 + 51*x^5 + 48*x^6 + 40*x^7 + 25*x^8 + 13*x^9 + 4*x^10 + x^11 - x^12 - x^13 + x^14) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 14 2018
Showing 1-10 of 16 results. Next

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