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 1-6 of 6 results.

A036838 Triangle read by rows: T(n,k) = value of Schoenheim bound L_1(n+2,k+2,k+1) on covering numbers (0 <= k <= n).

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 6, 6, 5, 1, 4, 7, 11, 9, 6, 1, 4, 11, 14, 18, 12, 7, 1, 5, 12, 25, 26, 27, 16, 8, 1, 5, 17, 30, 50, 44, 39, 20, 9, 1, 6, 19, 47, 66, 92, 70, 54, 25, 10, 1, 6, 24, 57, 113, 132, 158, 105, 72, 30, 11, 1, 7, 26, 78, 149, 245, 246
Offset: 0

Views

Author

N. J. A. Sloane, Jan 11 2002

Keywords

Comments

The relation with Schoenheim's notation is L(v,k,t,l) = psi(k,t,l,v). - R. J. Mathar, Aug 12 2012

Examples

			Triangle begins
  1;
  2,  1;
  2,  3,  1;
  3,  4,  4,  1;
  3,  6,  6,  5,  1;
  4,  7, 11,  9,  6,  1;
  4, 11, 14, 18, 12,  7,  1;
  5, 12, 25, 26, 27, 16,  8,  1;
  ...

References

  • W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of Jeffrey H. Dinitz and D. R. Stinson, editors, Contemporary Design Theory, Wiley, 1992. See Eq. 1.

Links

Crossrefs

Columns give A011975, A036831, A036832, A036833, A036834, A036835, A036836, A014125, A036830, A036837.

Programs

  • Maple
    L := proc(v,k,t,l)
    local i,t1;
    t1 := l;
    for i from v-t+1 to v do
        t1 := ceil(t1*i/(i-(v-k)));
    od:
    t1;
end;
A036838 := proc(n,k)
    L(n+2,k+2,k+1,1) ;
end proc:
  • Mathematica
    L[v_, k_, t_, l_] := Module[{i, t1}, t1 = l; For[i = v-t+1, i <= v, i++, t1 = Ceiling[t1*i/(i-(v-k))]]; t1]; A036838[n_, k_] := L[n+2, k+2, k+1, 1]; Table[A036838[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 16 2013, translated from Maple *)

A240115 Schoenheim lower bound L(n,4,2).

Original entry on oeis.org

1, 3, 3, 4, 6, 7, 8, 11, 12, 13, 18, 19, 20, 26, 27, 29, 35, 37, 39, 46, 48, 50, 59, 61, 63, 73, 75, 78, 88, 91, 94, 105, 108, 111, 124, 127, 130, 144, 147, 151, 165, 169, 173, 188, 192, 196, 213, 217, 221, 239, 243, 248, 266, 271, 276, 295, 300, 305, 326
Offset: 4

Views

Author

Colin Barker, Apr 01 2014

Keywords

Comments

Only differs from A011976 when n = 7, 9, 10, or 19. - Nathaniel Johnston, Jan 10 2024

Links

Crossrefs

Cf. A240116, A240117, A240118, A240119.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 4, 2], {n, 4, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=4, 100, s=concat(s, schoenheim(n, 4, 2))); s

Formula

Empirical g.f.: x^4*(x^15 -x^13 -x^12 +2*x^10 +x^7 +x^5 +2*x +1) / ( -x^16 +x^15 +x^13 -x^12 +x^4 -x^3 -x +1).
a(n) = ceiling((n/4)*ceiling((n-1)/3)). - Nathaniel Johnston, Jan 10 2024

A240116 Schoenheim lower bound L(n,5,2).

Original entry on oeis.org

1, 3, 3, 4, 4, 6, 7, 8, 8, 12, 12, 13, 14, 18, 19, 20, 21, 27, 28, 29, 30, 37, 38, 40, 41, 48, 50, 52, 53, 62, 63, 65, 67, 76, 78, 80, 82, 93, 95, 97, 99, 111, 113, 116, 118, 130, 133, 136, 138, 152, 154, 157, 160, 174, 177, 180, 183, 199, 202, 205, 208, 225
Offset: 5

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240117, A240118, A240119.
Cf. A011975, A011977, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 5, 2], {n, 5, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=5, 100, s=concat(s, schoenheim(n, 5, 2))); s

Formula

Empirical g.f.: x^5*(x^24 -x^21 -x^20 +2*x^17 +x^14 +x^12 -x^10 +2*x^9 +x^6 -x^4 +x^3 +2*x +1) / ( -x^25 +x^24 +x^21 -x^20 +x^5 -x^4 -x +1).
a(n) = ceiling((n/5)*ceiling((n-1)/4)). - Nathaniel Johnston, Jan 10 2024

A240117 Schoenheim lower bound L(n,6,2).

Original entry on oeis.org

1, 3, 3, 3, 4, 4, 6, 7, 7, 8, 8, 12, 12, 13, 14, 14, 19, 20, 20, 21, 22, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 50, 51, 52, 54, 55, 63, 65, 66, 68, 69, 79, 80, 82, 84, 85, 96, 98, 99, 101, 103, 114, 116, 118, 120, 122, 135, 137, 139, 141, 143, 157, 159, 161
Offset: 6

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240116, A240118, A240119.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 6, 2], {n, 6, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=6, 100, s=concat(s, schoenheim(n, 6, 2))); s

Formula

Empirical g.f.: x^6*(x^35 -x^31 -x^30 +2*x^26 +x^23 +x^20 -x^18 +x^17 +x^16 +x^13 -x^12 +2*x^11 +x^7 -x^5 +x^4 +2*x +1) / ( -x^36 +x^35 +x^31 -x^30 +x^6 -x^5 -x +1).

A240118 Schoenheim lower bound L(n,5,3).

Original entry on oeis.org

1, 4, 5, 7, 11, 14, 18, 27, 32, 37, 54, 61, 68, 94, 103, 116, 147, 163, 180, 221, 240, 260, 319, 342, 366, 438, 465, 500, 581, 619, 658, 756, 800, 844, 968, 1016, 1066, 1210, 1265, 1329, 1485, 1555, 1627, 1805, 1882, 1960, 2173, 2257, 2343, 2582, 2673, 2778
Offset: 5

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240116, A240117, A240119.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 5, 3], {n, 5, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=5, 100, s=concat(s, schoenheim(n, 5, 3))); s

A240119 Schoenheim lower bound L(n,6,3).

Original entry on oeis.org

1, 4, 4, 6, 7, 11, 14, 18, 19, 30, 32, 37, 42, 57, 64, 70, 77, 104, 112, 121, 130, 167, 178, 194, 205, 248, 267, 286, 301, 362, 378, 401, 425, 494, 520, 547, 574, 667, 697, 728, 759, 870, 904, 948, 984, 1105, 1153, 1202, 1242, 1394, 1438, 1492, 1547, 1711
Offset: 6

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240116, A240117, A240118.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 6, 3], {n, 6, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=6, 100, s=concat(s, schoenheim(n, 6, 3))); s
Showing 1-6 of 6 results.

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

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