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 1-4 of 4 results.

A286879 Number of minimal dominating sets in the n-Andrásfai graph.

Original entry on oeis.org

2, 5, 28, 66, 140, 272, 489, 828, 1339, 2088, 3160, 4662, 6726, 9512, 13211, 18048, 24285, 32224, 42210, 54634, 69936, 88608, 111197, 138308, 170607, 208824, 253756, 306270, 367306, 437880, 519087, 612104, 718193, 838704, 975078, 1128850, 1301652, 1495216, 1711377
Offset: 1

Views

Author

Eric W. Weisstein, Aug 02 2017

Keywords

Links

Crossrefs

Cf. A285272, A290587, A291053.

Programs

  • Magma
    [2,5,28] cat [(3*n-1)*(n^4-13*n^3+164*n^2-572*n+ 960)/120: n in [4..40]]; // Vincenzo Librandi, Sep 03 2017
  • Maple
    A286879:=n->(3*n - 1)*(n^4 - 13*n^3 + 164*n^2 - 572*n + 960)/120: 2,5,28,seq(A286879(n), n=4..100); # Wesley Ivan Hurt, Nov 30 2017
  • Mathematica
    Table[Piecewise[{{2, n == 1}, {5, n == 2}, {28, n == 3}}, (3 n - 1) (n^4 - 13 n^3 + 164 n^2 - 572 n + 960)/120], {n, 20}]
Join[{2, 5, 28}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {66, 140, 272, 489, 828, 1339}, 20]] (* Eric W. Weisstein, Aug 21 2017 *)
CoefficientList[Series[(2 - 7 x + 28 x^2 - 67 x^3 + 94 x^4 - 75 x^5 + 29 x^6 + x^7 - 2 x^8)/(-1 + x)^6, {x, 0, 20}], x] (* Eric W. Weisstein, Aug 21 2017 *)

Formula

From Eric W. Weisstein, Aug 21 2017: (Start)
a(n) = (3*n - 1)*(n^4 - 13*n^3 + 164*n^2 - 572*n + 960)/120 for n > 3.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 9.
G.f.: (x (2 - 7 x + 28 x^2 - 67 x^3 + 94 x^4 - 75 x^5 + 29 x^6 + x^7 - 2 x^8))/(-1 + x)^6.
(End)

Extensions

a(10)-a(20) from Andrew Howroyd, Aug 19 2017
a(21) and higher from Eric W. Weisstein, Aug 21 2017

A291053 Number of maximal irredundant sets in the n-Andrásfai graph.

Original entry on oeis.org

2, 10, 28, 88, 217, 493, 989, 1794, 3016, 4785, 7256, 10612, 15067, 20869, 28303, 37694, 49410, 63865, 81522, 102896, 128557, 159133, 195313, 237850, 287564, 345345, 412156, 489036, 577103, 677557, 791683, 920854, 1066534, 1230281, 1413750, 1618696, 1846977, 2100557
Offset: 1

Views

Author

Eric W. Weisstein, Aug 17 2017

Keywords

Links

Crossrefs

Cf. A285272, A290587, A291053.

Programs

  • Mathematica
    Table[Piecewise[{{2, n == 1}, {10, n == 2}, {28, n == 3}}, (-3120 + 10932 n - 4970 n^2 + 765 n^3 - 10 n^4 + 3 n^5)/120], {n, 20}]
Join[{2, 10, 28}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {88, 217, 493, 989, 1794, 3016}, 20]] (* Eric W. Weisstein, Aug 21 2017 *)
CoefficientList[Series[(2 - 2 x - 2 x^2 + 30 x^3 - 61 x^4 + 89 x^5 - 112 x^6 + 77 x^7 - 18 x^8)/(-1 + x)^6, {x, 0, 20}], x] (* Eric W. Weisstein, Aug 21 2017 *)

Formula

From Eric W. Weisstein, Aug 21 2017: (Start)
a(n) = (-3120 + 10932*n - 4970*n^2 + 765*n^3 - 10*n^4 + 3*n^5)/120 for n > 3.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 9.
G.f.: (x (2 - 2 x - 2 x^2 + 30 x^3 - 61 x^4 + 89 x^5 - 112 x^6 + 77 x^7 - 18 x^8))/(-1 + x)^6.
(End)

Extensions

a(9)-a(20) from Andrew Howroyd, Aug 19 2017
a(21) and above from Eric W. Weisstein, Aug 21 2017

A290587 Number of irredundant sets in the n-Andrásfai graph.

Original entry on oeis.org

3, 16, 81, 265, 729, 1786, 4060, 8833, 18786, 39586, 83273, 175463, 370615, 784290, 1661122, 3517669, 7441936, 15720066, 33145015, 69744491, 146458013, 306933394, 642004440, 1340415817, 2793811726, 5813791138, 12080174037, 25065845455, 51943066643, 107509343618, 222265656670, 459025904205, 947041760092, 1952064327682
Offset: 1

Views

Author

Eric W. Weisstein, Aug 07 2017

Keywords

Links

Crossrefs

Cf. A285272, A286879, A291053.

Programs

  • Mathematica
    Table[Piecewise[{{3, n == 1}, {16, n == 2}, {81, n == 3}}, (-45 (8 + 3 2^n) + (1772 + 405 2^n) n - 1010 n^2 + 25 n^3 + 50 n^4 + 3 n^5)/120], {n, 20}] (* Eric W. Weisstein, Aug 21 2017 *)
Join[{3, 16, 81}, LinearRecurrence[{10, -43, 104, -155, 146, -85, 28, -4}, {265, 729, 1786, 4060, 8833, 18786, 39586, 83273}, 20]] (* Eric W. Weisstein, Aug 21 2017 *)
CoefficientList[Series[-((-3 + 14 x - 50 x^2 + 169 x^3 - 363 x^4 + 491 x^5 - 461 x^6 + 260 x^7 - 46 x^8 - 22 x^9 + 8 x^10)/((-1 + x)^6 (-1 + 2 x)^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 21 2017 *)

Formula

From Eric W. Weisstein, Aug 21 2017: (Start)
a(n) = (-45*(8 + 3*2^n) + (1772 + 405*2^n) n - 1010*n^2 + 25*n^3 + 50*n^4 + 3*n^5)/120 for n > 3.
a(n) = 10*a(n-1) - 43*a(n-2) + 104*a(n-3) - 155*a(n-4) + 146*a(n-5) - 85*a(n-6) + 28*a(n-7) - 4*a(n-8) for n > 11.
G.f.: -((x (-3 + 14 x - 50 x^2 + 169 x^3 - 363 x^4 + 491 x^5 - 461 x^6 + 260 x^7 - 46 x^8 - 22 x^9 + 8 x^10))/((-1 + x)^6 (-1 + 2 x)^2)).
(End)

Extensions

a(9)-a(20) from Andrew Howroyd, Aug 19 2017
a(21) and above from Eric W. Weisstein, Aug 21 2017

A302759 Number of total dominating sets in the n-Andrásfai graph.

Original entry on oeis.org

1, 11, 131, 1365, 12883, 113935, 967455, 8013983, 65410751, 529283583, 4261449727, 34213027327, 274240586751, 2196272295935, 17580376055807, 140687025184767, 1125685164621823, 9006288735567871, 72053745778425855, 576444534576513023, 4611617848860868607
Offset: 1

Views

Author

Eric W. Weisstein, Apr 12 2018

Keywords

Links

Crossrefs

Cf. A285272, A287429, A302762.

Programs

  • Mathematica
    Join[{1}, Table[(8^(n + 1) + (2^n (n - 2) - 4^(n + 1) ) (3 n - 1) - 16)/16, {n, 2, 20}]]
Join[{1}, LinearRecurrence[{23, -210, 996, -2664, 4032, -3200, 1024}, {11, 131, 1365, 12883, 113935, 967455, 8013983}, 20]]
CoefficientList[Series[(-1 + 12 x - 88 x^2 + 334 x^3 - 706 x^4 + 928 x^5 - 672 x^6 + 256 x^7)/((-1 + 2 x)^3 (-1 + 4 x)^2 (1 - 9 x + 8 x^2)), {x, 0, 20}], x]

Formula

a(n) = (8^(n + 1) + (2^n*(n - 2) - 4^(n + 1))*(3*n - 1))/16 - 1 for n > 1.
a(n) = 23*a(n-1) - 210*a(n-2) + 996*a(n-3) - 2664*a(n-4) + 4032*a(n-5) - 3200*a(n-6) + 1024*a(n-7) for n > 8.
G.f.: x*(-1 + 12*x - 88*x^2 + 334*x^3 - 706*x^4 + 928*x^5 - 672*x^6 + 256*x^7)/((-1 + 2*x)^3*(-1 + 4*x)^2*(1 - 9*x + 8*x^2)).
E.g.f.: (1 - 8*exp(x) + 4*exp(8*x) + exp(4*x)*(2 - 24*x) + 2*x + exp(2*x)*(1 - 4*x + 6*x^2))/8. - Stefano Spezia, Aug 29 2025

Extensions

a(9)-a(21) from Andrew Howroyd, Apr 18 2018
Showing 1-4 of 4 results.

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