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.

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).

A367654 G.f. A(x) satisfies A(x) = 1 / (1 - x * (1 + x + x^2 + x^3 + x^4) * A(x^5)).

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1025, 2051, 4104, 8212, 16432, 32882, 65798, 131664, 263464, 527200, 1054948, 2110989, 4224165, 8452706, 16914168, 33845864, 67726796, 135523764, 271187944, 542656864, 1085875984, 2172877052, 4348005437, 8700515871
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Links

Crossrefs

Cf. A127680, A367652, A367653.
Cf. A367661.

Programs

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

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} a(floor(k/5)) * 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).

A367658 G.f. A(x) satisfies A(x) = 1 / (1 - x - x * (1 + x + x^2 + x^3 + x^4) * A(x^5)).

Original entry on oeis.org

1, 2, 5, 13, 34, 89, 234, 615, 1616, 4246, 11156, 29314, 77026, 202394, 531811, 1397387, 3671781, 9647988, 25351094, 66612640, 175031647, 459913889, 1208471657, 3175385173, 8343655339, 21923823599, 57607130438, 151368736483, 397737124030, 1045095727865
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Crossrefs

Cf. A367655, A367656, A367657.
Cf. A367654, 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, v[j\5+1]*v[i-j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} a(floor(k/5)) * a(n-1-k).
Showing 1-4 of 4 results.

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