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 1-2 of 2 results.

A291986 Expansion of 1/((1-x)*(1-2*x^2)*(1-3*x^3)).

Original entry on oeis.org

1, 1, 3, 6, 10, 16, 33, 45, 79, 130, 198, 300, 517, 721, 1155, 1806, 2674, 3976, 6441, 9045, 13975, 21370, 31230, 46020, 72301, 101881, 154443, 233286, 338410, 496096, 765393, 1080765, 1619359, 2427250, 3504438, 5120220, 7806037, 11037601, 16409235, 24466686
Offset: 0

Views

Author

Seiichi Manyama, Sep 07 2017

Keywords

Links

Crossrefs

Cf. A291960, A291987, A291988.

Programs

  • Mathematica
    CoefficientList[Series[1/((1-x)(1-2x^2)(1-3x^3)),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,1,-3,-6,6},{1,1,3,6,10,16},40] (* Harvey P. Dale, Sep 15 2023 *)
  • PARI
    Vec(1/((1-x)*(1-2*x^2)*(1-3*x^3)) + O(x^100))

A291988 Expansion of 1/((1-x)*(1-2*x^2)*(1-3*x^3)*(1-4*x^4)*(1-5*x^5)).

Original entry on oeis.org

1, 1, 3, 6, 14, 25, 50, 84, 165, 280, 503, 826, 1477, 2386, 4067, 6625, 11032, 17605, 29039, 45820, 74708, 117410, 187691, 293155, 467733, 724421, 1140157, 1763581, 2758717, 4238285, 6599926, 10082054, 15609032, 23819315, 36607147, 55644926, 85380815, 129185681
Offset: 0

Views

Author

Seiichi Manyama, Sep 07 2017

Keywords

Links

Crossrefs

Cf. A291960, A291986, A291987.

Programs

  • GAP
    a:=[1,1,3,6,14,25,50,84,165,280,503,826,1477,2386,4067];;
for n in [16..10^2] do a[n]:=a[n-1]+2*a[n-2]+a[n-3]+a[n-4]-5*a[n-5]-7*a[n-6]-14*a[n-7]+7*a[n-8]+19*a[n-9]+26*a[n-10]+10*a[n-11]+20*a[n-12]-60*a[n-13]-120*a[n-14]+120*a[n-15]; od; a; # Muniru A Asiru, Sep 07 2017
  • Mathematica
    CoefficientList[Series[1/Times@@Table[1-n x^n,{n,5}],{x,0,40}],x] (* or *) LinearRecurrence[{1,2,1,1,-5,-7,-14,7,19,26,10,20,-60,-120,120},{1,1,3,6,14,25,50,84,165,280,503,826,1477,2386,4067},40] (* Harvey P. Dale, Aug 10 2021 *)
  • PARI
    Vec(1/((1-x)*(1-2*x^2)*(1-3*x^3)*(1-4*x^4)*(1-5*x^5)) + O(x^100))

Formula

a(n) = a(n-1) + 2*a(n-2) + a(n-3) + a(n-4) - 5*a(n-5) - 7*a(n-6) - 14*a(n-7) + 7*a(n-8) + 19*a(n-9) + 26*a(n-10) + 10*a(n-11) + 20*a(n-12) - 60*a(n-13) - 120*a(n-14) + 120*a(n-15) for n >= 16. - Muniru A Asiru, Sep 07 2017
Showing 1-2 of 2 results.

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