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 1-5 of 5 results.

A151610 Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

Original entry on oeis.org

0, 252, 4935, 56560, 572215, 5503260, 51377823, 469758912, 4227854463, 37580958940, 330712475863, 2886218015856, 25013889523623, 215504279034492, 1847179534652655, 15762598695784192, 133982088914258095, 1134907106097349116, 9583660007044397799, 80704505322479268720
Offset: 1

Views

Author

R. H. Hardin, May 21 2009

Keywords

Links

Crossrefs

Cf. A151583.

Programs

  • PARI
    a(n) = if(n <= 1, 0, n*(7*8^n/2 - 49*n)) \\ Andrew Howroyd, May 04 2020
  • PARI
    concat(0, Vec(7*x^2*(36 + 21*x - 1175*x^2 + 624*x^3 - 192*x^4) / ((1 - x)^3*(1 - 8*x)^2) + O(x^20))) \\ Colin Barker, Jul 16 2020

Formula

a(n) = n*((7/2)*8^n - 49*n) for n > 1. - Andrew Howroyd, May 04 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: 7*x^2*(36 + 21*x - 1175*x^2 + 624*x^3 - 192*x^4) / ((1 - x)^3*(1 - 8*x)^2).
a(n) = 19*a(n-1) - 115*a(n-2) + 241*a(n-3) - 208*a(n-4) + 64*a(n-5) for n>6.
(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 04 2020

A151590 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

Original entry on oeis.org

0, 12, 207, 1392, 7455, 36540, 171591, 785856, 3538215, 15727740, 69204927, 301988592, 1308621327, 5637142812, 24159189015, 103079212800, 438086661591, 1855425868956, 7834020344655, 32985348829680, 138538465095807, 580542139461372, 2427721674124647
Offset: 1

Views

Author

R. H. Hardin, May 21 2009

Keywords

Links

Crossrefs

Cf. A151583.

Programs

  • PARI
    a(n) = if(n <= 1, 0, n*(3*4^n/2 - 9*n)) \\ Andrew Howroyd, May 04 2020
  • PARI
    concat(0, Vec(3*x^2*(4 + 25*x - 123*x^2 + 56*x^3 - 16*x^4) / ((1 - x)^3*(1 - 4*x)^2) + O(x^40))) \\ Colin Barker, Jul 16 2020

Formula

a(n) = n*((3/2)*4^n - 9*n) for n > 1. - Andrew Howroyd, May 04 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: 3*x^2*(4 + 25*x - 123*x^2 + 56*x^3 - 16*x^4) / ((1 - x)^3*(1 - 4*x)^2).
a(n) = 11*a(n-1) - 43*a(n-2) + 73*a(n-3) - 56*a(n-4) + 16*a(n-5) for n>6.
(End)

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 04 2020

A151597 Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

Original entry on oeis.org

0, 36, 606, 4744, 30850, 186924, 1092966, 6248976, 35154954, 195310900, 1074216814, 5859372696, 31738278546, 170898434364, 915527340150, 4882812495904, 25939941401626, 137329101557316, 724792480462974, 3814697265618600, 20027160644524194, 104904174804679756
Offset: 1

Views

Author

R. H. Hardin, May 21 2009

Keywords

Links

Crossrefs

Cf. A151583.

Programs

  • Magma
    [0] cat [ n*(2*5^n - 16*n) : n in [2..30]]; // Wesley Ivan Hurt, Jul 16 2020
  • PARI
    a(n) = if(n <= 1, 0, n*(2*5^n - 16*n)) \\ Andrew Howroyd, May 04 2020
  • PARI
    concat(0, Vec(2*x^2*(18 + 69*x - 523*x^2 + 255*x^3 - 75*x^4) / ((1 - x)^3*(1 - 5*x)^2) + O(x^40))) \\ Colin Barker, Jul 16 2020

Formula

a(n) = n*(2*5^n - 16*n) for n > 1. - Andrew Howroyd, May 04 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: 2*x^2*(18 + 69*x - 523*x^2 + 255*x^3 - 75*x^4) / ((1 - x)^3*(1 - 5*x)^2).
a(n) = 13*a(n-1) - 58*a(n-2) + 106*a(n-3) - 85*a(n-4) + 25*a(n-5) for n>6.
(End)

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 04 2020

A151603 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

Original entry on oeis.org

0, 80, 1395, 12560, 96575, 698940, 4897655, 33590720, 226746135, 1511651900, 9976916015, 65303466480, 424472551295, 2742745738460, 17631936915975, 112844396291840, 719383026394055, 4570198050070620, 28944587650489535, 182807922003138800, 1151689908619826415
Offset: 1

Views

Author

R. H. Hardin, May 21 2009

Keywords

Links

Crossrefs

Cf. A151583.

Programs

  • Magma
    [0] cat [n*((5/2)*6^n - 25*n) : n in [2..30]]; // Wesley Ivan Hurt, Jul 17 2020
  • PARI
    a(n) = if(n <= 1, 0, n*(5*6^n/2 - 25*n)) \\ Andrew Howroyd, May 04 2020
  • PARI
    Vec(5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2) + O(x^21)) \\ Colin Barker, Jul 17 2020

Formula

a(n) = n*((5/2)*6^n - 25*n) for n > 1. - Andrew Howroyd, May 04 2020
From Colin Barker, Jul 17 2020: (Start)
G.f.: 5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2).
a(n) = 15*a(n-1) - 75*a(n-2) + 145*a(n-3) - 120*a(n-4) + 36*a(n-5) for n>5.
(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 04 2020

A151607 Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

Original entry on oeis.org

0, 150, 2763, 28236, 251205, 2116386, 17292639, 138352920, 1089544473, 8474253870, 65251778163, 498286334052, 3778671399789, 28485369052602, 213640267939335, 1595180667331632, 11864156213337153, 87934334287152582, 649737025566256155, 4787535977856705660
Offset: 1

Views

Author

R. H. Hardin, May 21 2009

Keywords

Links

Crossrefs

Cf. A151583.

Programs

  • PARI
    a(n) = if(n <= 1, 0, n*(3*7^n - 36*n)) \\ Andrew Howroyd, May 04 2020
  • PARI
    concat(0, Vec(3*x^2*(50 + 71*x - 1545*x^2 + 805*x^3 - 245*x^4) / ((1 - x)^3*(1 - 7*x)^2) + O(x^40))) \\ Colin Barker, Jul 17 2020

Formula

a(n) = n*(3*7^n - 36*n) for n > 1. - Andrew Howroyd, May 04 2020
From Colin Barker, Jul 17 2020: (Start)
G.f.: 3*x^2*(50 + 71*x - 1545*x^2 + 805*x^3 - 245*x^4) / ((1 - x)^3*(1 - 7*x)^2).
a(n) = 17*a(n-1) - 94*a(n-2) + 190*a(n-3) - 161*a(n-4) + 49*a(n-5) for n>6.
(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 04 2020
Showing 1-5 of 5 results.

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