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.

A341698 a(1) = a(2) = 1; a(n+1) = -Sum_{d|n, d < n} a(n/d) * a(d).

Original entry on oeis.org

1, 1, -1, 1, -2, 2, 0, 0, -2, 1, 3, -3, 1, -1, 1, -5, 4, -4, 12, -12, 14, -14, 8, -8, 10, -14, 12, -16, 18, -18, 26, -26, 36, -30, 22, -22, 24, -24, 0, 2, 20, -20, -10, 10, 12, -18, 2, -2, 14, -14, -2, 10, 16, -16, -8, 20, 14, 10, -46, 46, -52, 52, -104, 132, -70, 74, -186, 186, -134, 150
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 17 2021

Keywords

Crossrefs

Cf. A038044, A325303, A341697.

Programs

  • Mathematica
    a[1] = a[2] = 1; a[n_] := a[n] = -Sum[If[d < (n - 1), a[(n - 1)/d] a[d], 0], {d, Divisors[n - 1]}]; Table[a[n], {n, 70}]
  • PARI
    A341698(n) = if(n<3, 1, sumdiv(n-1,d,if(d<(n-1), -A341698((n-1)/d)*A341698(d), 0))); \\ Antti Karttunen, Feb 17 2021

A351787 a(1) = 1; a(n+1) = a(n) + Sum_{d|n} a(n/d) * a(d).

Original entry on oeis.org

1, 2, 6, 18, 58, 174, 546, 1638, 4986, 14994, 45214, 135642, 407838, 1223514, 3672726, 11018874, 33063498, 99190494, 297593514, 892780542, 2678403690, 8035217622, 24105833722, 72317501166, 216953071986, 650859219322, 1952579289318, 5857737927786, 17573218697070
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

Crossrefs

Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351788.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[a[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 29}]

Formula

G.f.: x * ( 1 + Sum_{i>=1} Sum_{j>=1} a(i) * a(j) * x^(i*j) ) / (1 - x).

A351788 a(1) = 1; a(n) = a(n-1) + Sum_{d|n, 1 < d < n} a(n/d) * a(d).

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 4, 8, 9, 13, 13, 25, 25, 33, 37, 57, 57, 83, 83, 117, 125, 151, 151, 233, 237, 287, 305, 387, 387, 503, 503, 649, 675, 789, 805, 1073, 1073, 1239, 1289, 1607, 1607, 1955, 1955, 2309, 2419, 2721, 2721, 3465, 3481, 4007, 4121, 4795, 4795, 5643, 5695
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

Crossrefs

Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351787.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[If[1 < d < n, a[n/d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}]

Formula

G.f.: ( x + Sum_{i>=2} Sum_{j>=2} a(i) * a(j) * x^(i*j) ) / (1 - x).

A351797 a(1) = 1; a(n+1) = -a(n) + 2 * Sum_{d|n} a(n/d) * a(d).

Original entry on oeis.org

1, 1, 3, 9, 29, 87, 273, 819, 2493, 7497, 22607, 67821, 203919, 611757, 1836363, 5509437, 16531749, 49595247, 148796757, 446390271, 1339201845, 4017608811, 12052916861, 36158750583, 108476535993, 325429609661, 976289644659, 2928868963893, 8786609348535
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

Crossrefs

Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351787, A351788.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[a[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 29}]

Formula

G.f.: x * ( 1 + 2 * Sum_{i>=1} Sum_{j>=2} a(i) * a(j) * x^(i*j) ) / (1 - x).
a(n) = A351787(n) / 2 for n > 1.
Showing 1-4 of 4 results.

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

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