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.

A367659 G.f. A(x) satisfies A(x) = 1 / (1 - x - x * A(x^3)).

Original entry on oeis.org

1, 2, 4, 8, 18, 40, 88, 196, 436, 968, 2152, 4784, 10632, 23634, 52536, 116776, 259576, 577000, 1282576, 2850968, 6337264, 14086744, 31312644, 69603152, 154716976, 343911796, 764462500, 1699281320, 3777238312, 8396213840, 18663478600, 41486012712, 92216959616
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Links

Crossrefs

Cf. A349365, A367660, A367661.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, (i-1)\3, v[j+1]*v[i-3*j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-1)/3)} a(k) * a(n-1-3*k).
a(0) = 1, a(1) = 2, a(2) = 4; a(n) = a(n-3) + Sum_{k=0..n-1} a(floor(k/3)) * a(n-1-k).

A367660 G.f. A(x) satisfies A(x) = 1 / (1 - x - x * A(x^4)).

Original entry on oeis.org

1, 2, 4, 8, 16, 34, 72, 152, 320, 676, 1428, 3016, 6368, 13448, 28400, 59976, 126656, 267472, 564848, 1192848, 2519056, 5319746, 11234248, 23724504, 50101440, 105804296, 223437672, 471856016, 996466240, 2104338904, 4443946064, 9384731992, 19818691136
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Crossrefs

Cf. A349365, A367659, A367661.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, (i-1)\4, v[j+1]*v[i-4*j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-1)/4)} a(k) * a(n-1-4*k).
a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8; a(n) = a(n-4) + Sum_{k=0..n-1} a(floor(k/4)) * a(n-1-k).

A367661 G.f. A(x) satisfies A(x) = 1 / (1 - x - x * A(x^5)).

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 66, 136, 280, 576, 1184, 2436, 5012, 10312, 21216, 43648, 89800, 184752, 380104, 782016, 1608896, 3310096, 6810096, 14010896, 28825616, 59304992, 122012384, 251024768, 516451136, 1062531712, 2186022176, 4497459138, 9252943048
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Links

Crossrefs

Cf. A349365, A367659, A367660.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, (i-1)\5, v[j+1]*v[i-5*j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-1)/5)} a(k) * a(n-1-5*k).
a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8, a(4) = 16; a(n) = a(n-5) + Sum_{k=0..n-1} a(floor(k/5)) * a(n-1-k).

A218032 G.f. A(x) satisfies A(x) = 1 + x / (1 - x * A(x^2)).

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 35, 57, 94, 154, 254, 417, 687, 1129, 1859, 3057, 5032, 8277, 13623, 22412, 36883, 60684, 99862, 164312, 270384, 444899, 732093, 1204629, 1982228, 3261701, 5367131, 8831505, 14532200, 23912499, 39347839, 64746320, 106539481, 175309363, 288469809
Offset: 0

Views

Author

Joerg Arndt, Oct 19 2012

Keywords

Comments

What does this sequence count?

Links

Crossrefs

Cf. A319436, A349365.

Programs

  • PARI
    N=66;  R=O('x^N);  x='x+R;
F = 1 + x;
for (k=1,N+1, F = 1 + x / (1 - x * subst(F,'x,'x^2) ) + R; );
Vec(F)

A351938 a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..floor((n-1)/2)} a(k) * a(n-2*k-1).

Original entry on oeis.org

1, 1, 1, 3, 5, 9, 17, 35, 65, 125, 241, 463, 885, 1701, 3265, 6271, 12033, 23105, 44353, 85147, 163445, 313777, 602353, 1156339, 2219809, 4261389, 8180561, 15704215, 30147333, 57873821, 111100225, 213278943, 409431169, 785984353, 1508852673, 2896541859
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2022

Keywords

Crossrefs

Cf. A000621, A001003, A319436, A349365.

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 35}]
nmax = 35; A[] = 0; Do[A[x] = 1/(1 + x - 2 x A[x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(x^2)).
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.