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.

Previous Showing 11-18 of 18 results.

A055066 Number of 7-covers of an unlabeled n-set.

Original entry on oeis.org

1, 7, 62, 664, 8609, 127415, 2004975, 31500927, 474504448, 6708348262, 88249739792, 1078567590128, 12269901302433, 130370516668917, 1298891291366245, 12182760243381355, 107979270564656625, 907568508195185203, 7256984238345563764, 55365443728411530716, 404091280028746802188
Offset: 0

Views

Author

Vladeta Jovovic, Jun 12 2000

Keywords

Comments

Number of 7 X n binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

Links

Crossrefs

Column 7 of A055080.
Cf. A005748, A002620, A005783, A005784, A005785, A005786.

Programs

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 08 2022
Terms a(17) and beyond from Andrew Howroyd, Feb 28 2023

A005784 Number of 4-covers of an unlabeled n-set.

Original entry on oeis.org

1, 4, 17, 65, 230, 736, 2197, 6093, 15864, 38960, 90837, 202005, 430577, 883057, 1748909, 3355213, 6252575, 11345602, 20089514, 34778306, 58964020, 98053576, 160151566, 257229974, 406739271, 633795181, 974126408, 1477999320, 2215409037, 3282874359, 4812278064
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of 4 X n binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column 4 of A055080.
First differences of A006148.
Cf. A002620, A005783, A005785, A005786, A055066.

Programs

Formula

G.f.: (x^20 - x^19 + 4*x^18 + 9*x^17 + 23*x^16 + 39*x^15 + 90*x^14 + 131*x^13 + 204*x^12 + 238*x^11 + 252*x^10 + 238*x^9 + 204*x^8 + 131*x^7 + 90*x^6 + 39*x^5 + 23*x^4 + 9*x^3 + 4*x^2 - x + 1)/((1 - x^4)^3*(1 - x^3)^4*(1 - x^2)^3*(1 - x)^5).
a(n) ~ n^14/2092278988800. - Stefano Spezia, Aug 08 2022
a(n) = n^14/2092278988800 + n^13/19926466560 + n^12/418037760 + n^11/14598144 + 689*n^10/522547200 + 253*n^9/13934592 + 2184839*n^8/11705057280 + 10313*n^7/6967296 + 2319707*n^6/250822656 + 1817221*n^5/39813120 + 2405336243*n^4/13795246080 + 151784975*n^3/306561024 + 93746545019*n^2/95103590400 + 924100468541*n/717352796160 + 1 + (n^2/486 + 5*n/162 + 233/2187)*floor(n/3) + (n^2/256 + 15*n/256 + 101/512)*floor(n/4) - (n^3/1458 + 7*n^2/486 + 22*n/243 + 356/2187)*floor((n+1)/3) + (n^5/122880 + 5*n^4/16384 + 125*n^3/24576 + 359*n^2/8192 + 10967*n/61440 + 8461/32768)*floor(n/2) + (n/256 + 15/512)*floor((n+1)/4). - Vaclav Kotesovec, Aug 09 2022

Extensions

More terms from Vladeta Jovovic, Jun 03 2000
a(0)=1 prepended by Alois P. Heinz, Aug 08 2022

A005785 Number of 5-covers of an unlabeled n-set.

Original entry on oeis.org

1, 5, 28, 156, 863, 4571, 22952, 108182, 477136, 1969270, 7625579, 27804973, 95858868, 313747418, 978734539, 2920530663, 8363945469, 23057872913, 61357278239, 157985305473, 394486861086, 957156158394, 2260761331227
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of 5 X n binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column 5 of A055080.
First differences of A052264.
Cf. A002620, A005783, A005784, A055066.

Programs

Formula

G.f.: - (x^68 - 2*x^67 + 10*x^66 + 32*x^65 + 175*x^64 + 794*x^63 + 3441*x^62 + 13186*x^61 + 46027*x^60 + 146118*x^59 + 427347*x^58 + 1155432*x^57 + 2912873*x^56 + 6875608*x^55 + 15281029*x^54 + 32094658*x^53 + 63945531*x^52 + 121210914*x^51 + 219194198*x^50 + 378998758*x^49 + 627863648*x^48 + 998282344*x^47 + 1525746624*x^46 + 2244502676*x^45 + 3181886869*x^44 + 4351201210*x^43 + 5744918381*x^42 + 7328807372*x^41 + 9039504349*x^40 + 10785767638*x^39 + 12455264802*x^38 + 13925287384*x^37 + 15077477135*x^36 + 15812782150*x^35 + 16065602576*x^34 + 15812782150*x^33 + 15077477135*x^32 + 13925287384*x^31 + 12455264802*x^30 + 10785767638*x^29 + 9039504349*x^28 + 7328807372*x^27 + 5744918381*x^26 + 4351201210*x^25 + 3181886869*x^24 + 2244502676*x^23 + 1525746624*x^22 + 998282344*x^21 + 627863648*x^20 + 378998758*x^19 + 219194198*x^18 + 121210914*x^17 + 63945531*x^16 + 32094658*x^15 + 15281029*x^14 + 6875608*x^13 + 2912873*x^12 + 1155432*x^11 + 427347*x^10 + 146118*x^9 + 46027*x^8 + 13186*x^7 + 3441*x^6 + 794*x^5 + 175*x^4 + 32*x^3 + 10*x^2 - 2*x + 1)/((x^6 - 1)^2*(x^4 + x^3 + x^2 + x + 1)^6*(x^3 - x^2 + x - 1)^6*(x^2 + x + 1)^6*(x + 1)^10*(x - 1)^23).
a(n) = n^30/(30!*5!) + O(n^29). - Vaclav Kotesovec, Aug 09 2022

Extensions

More terms from Vladeta Jovovic, Jun 03 2000
a(0) = 1 prepended by Stefano Spezia, Aug 09 2022

A005786 Number of 6-covers of an unlabeled n-set.

Original entry on oeis.org

1, 6, 43, 336, 2864, 25326, 223034, 1890123, 15115098, 112980937, 787320629, 5121184083, 31188412225, 178517111561, 964196387369, 4933278065881, 23997707450765, 111358094980387, 494444748602595, 2106504840061571
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of 6 X n binary matrices with at least one 1 in every column up to row and column permutations.

References

  • R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column 6 of A055080.
Cf. A002620, A005783, A005784, A005785, A055066.

Programs

Extensions

More terms from Vladeta Jovovic, Jun 12 2000
a(0)=1 prepended by Alois P. Heinz, Aug 08 2022

A005745 Number of n-covers of an unlabeled 3-set.

Original entry on oeis.org

1, 6, 23, 65, 156, 336, 664, 1229, 2159, 3629, 5877, 9221, 14070, 20951, 30530, 43634, 61283, 84725, 115461, 155294, 206368, 271210, 352784, 454550, 580509, 735280, 924163, 1153207, 1429292, 1760218, 2154776, 2622859, 3175555, 3825247
Offset: 1

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

Comments

Number of n X 3 binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

  • R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A diagonal of A055080.
First differences give A055609.
Cf. A002623, A002727.
Cf. A005744, A005746, A005747, A005748, A005771.

Programs

Formula

a(n) = A002727(n) - A002623(n).
G.f.: -x*(x^8-x^7-x^6-2*x^5+2*x^4+x^3-3*x^2-2*x-1)/((x^3-1)^2*(x^2-1)^2*(x-1)^4).

Extensions

More terms from Vladeta Jovovic, May 26 2000

A005746 Number of n-covers of an unlabeled 4-set.

Original entry on oeis.org

1, 9, 51, 230, 863, 2864, 8609, 23883, 61883, 151214, 350929, 778113, 1656265, 3398229, 6743791, 12983181, 24311044, 44377016, 79124476, 138048542, 236050912, 396137492, 653285736, 1059923072, 1693592112, 2667563553, 4145373780, 6360553548, 9643151582
Offset: 1

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

Comments

Number of n X 4 binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A diagonal of A055080.
First differences give A055082.
Cf. A002727, A006148.
Cf. A005744, A005745, A005747, A005748, A005771.

Programs

  • Mathematica
    Rest@ CoefficientList[Series[x (1 + 3 x + 9 x^2 + 26 x^3 + 35 x^4 + 92 x^5 + 127 x^6 + 201 x^7 + 242 x^8 + 253 x^9 + 248 x^10 + 205 x^11 + 123 x^12 + 86 x^13 + 31 x^14 + 24 x^15 + 19 x^16 + 5 x^17 + 3 x^18 -
2 x^19 - 4 x^20 + 2 x^21 - 4 x^22 + 3 x^23 - x^25 + 2 x^26 - x^27)/((1 - x)^16 (1 + x)^6 (1 + x^2)^3 (1 + x + x^2)^4), {x, 0, 29}], x] (* Michael De Vlieger, Aug 23 2016 *)
  • PARI
    Vec(x*(1 +3*x +9*x^2 +26*x^3 +35*x^4 +92*x^5 +127*x^6 +201*x^7 +242*x^8 +253*x^9 +248*x^10 +205*x^11 +123*x^12 +86*x^13 +31*x^14 +24*x^15 +19*x^16 +5*x^17 +3*x^18 -2*x^19 -4*x^20 +2*x^21 -4*x^22 +3*x^23 -x^25 +2*x^26 -x^27) / ((1 -x)^16*(1 +x)^6*(1 +x^2)^3*(1 +x +x^2)^4) + O(x^40)) \\ Colin Barker, Aug 23 2016
  • PARI
    Vec(G(4, x) - G(3, x) + O(x^40)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023

Formula

a(n) = A006148(n) - A002727(n).
G.f.: x*(1 +3*x +9*x^2 +26*x^3 +35*x^4 +92*x^5 +127*x^6 +201*x^7 +242*x^8 +253*x^9 +248*x^10 +205*x^11 +123*x^12 +86*x^13 +31*x^14 +24*x^15 +19*x^16 +5*x^17 +3*x^18 -2*x^19 -4*x^20 +2*x^21 -4*x^22 +3*x^23 -x^25 +2*x^26 -x^27) / ((1 -x)^16*(1 +x)^6*(1 +x^2)^3*(1 +x +x^2)^4). - Corrected by Colin Barker, Aug 23 2016

Extensions

More terms and g.f. from Vladeta Jovovic, May 26 2000
a(19) onwards corrected by Sean A. Irvine, Aug 22 2016

A005747 Number of n-covers of an unlabeled 6-set.

Original entry on oeis.org

1, 16, 196, 2197, 22952, 223034, 2004975, 16642937, 127654604, 907349654, 6000728764, 37093282121, 215296646264, 1178514299094, 6108871834312, 30098215339608, 141433252447082, 635816643771438, 2742163498527536, 11374522802412498, 45482770393453638
Offset: 1

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

Comments

Number of n X 6 binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

  • R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A diagonal of A055080.
First differences give A055084.

Programs

Extensions

Corrected and extended by Vladeta Jovovic, Jun 13 2000
Terms a(20) and beyond from Andrew Howroyd, Feb 28 2023

A005771 Number of n-covers of an unlabeled 5-set.

Original entry on oeis.org

1, 12, 103, 736, 4571, 25326, 127415, 588687, 2518997, 10053739, 37656707, 133084998, 445949359, 1422934989, 4340110439, 12697803333, 35744330644, 97081519369, 255032046536, 649459943602, 1606518048420, 3867119228081, 9073566868140, 20783186834063
Offset: 1

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

Comments

Number of n X 5 binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

  • R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A diagonal of A055080.
First differences give A055083.
Cf. A006148, A052264.

Programs

Formula

a(n) = A052264(n) - A006148(n). - Andrew Howroyd, Feb 28 2023

Extensions

More terms from Vladeta Jovovic, Jun 13 2000
Terms a(21) and beyond from Andrew Howroyd, Feb 28 2023
Previous Showing 11-18 of 18 results.

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

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