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 1-8 of 8 results.

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).

A367652 G.f. A(x) satisfies A(x) = 1 / (1 - x * (1 + x + x^2) * A(x^3)).

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 32, 65, 131, 264, 534, 1078, 2176, 4396, 8877, 17925, 36202, 73108, 147636, 298152, 602108, 1215933, 2455552, 4958915, 10014374, 20223760, 40841302, 82477816, 166561622, 336366426, 679282324, 1371791274, 2770293218, 5594527784, 11297988864
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Crossrefs

Cf. A127680, A367653, A367654.
Cf. A367659.

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\3+1]*v[i-j])); v;

Formula

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

A367656 G.f. A(x) satisfies A(x) = 1 / (1 - x - x * (1 + x + x^2) * A(x^3)).

Original entry on oeis.org

1, 2, 5, 13, 35, 94, 252, 678, 1823, 4900, 13176, 35427, 95250, 256105, 688599, 1851450, 4978062, 13384681, 35987808, 96761612, 260166110, 699517054, 1880814358, 5057006914, 13596939262, 36558534049, 98296122593, 264291989596, 710610490247, 1910641595588
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Crossrefs

Cf. A367655, A367657, A367658.
Cf. A367652, A367659.

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\3+1]*v[i-j])); v;

Formula

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

A367691 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - x * A(x^3))).

Original entry on oeis.org

1, 2, 3, 4, 7, 12, 19, 31, 52, 86, 141, 233, 386, 639, 1057, 1749, 2896, 4795, 7937, 13138, 21751, 36010, 59613, 98688, 163380, 270479, 447779, 741300, 1227231, 2031697, 3363494, 5568295, 9218373, 15261119, 25264942, 41826373, 69244006, 114634194, 189778123
Offset: 0

Views

Author

Seiichi Manyama, Nov 27 2023

Keywords

Crossrefs

Cf. A007317, A351972, A367692.
Cf. A367659.

Programs

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

Formula

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

A367666 G.f. A(x) satisfies A(x) = 1 / (1 - x - x^2 * A(x^3)).

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 26, 46, 79, 138, 241, 418, 729, 1270, 2209, 3849, 6703, 11669, 20325, 35393, 61629, 107329, 186900, 325464, 566779, 986987, 1718745, 2993062, 5212135, 9076470, 15805899, 27524544, 47931568, 83468632, 145353195, 253119779, 440785795
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Crossrefs

Cf. A367659, A367667.
Cf. A319436.

Programs

  • Maple
    A367666 := proc(n)
    option remember;
    if n = 0 then
        1;
    else
        procname(n-1) + add(procname(k) * procname(n-2-3*k),k=0..floor((n-2)/3)) ;
    end if;
end proc:
seq(A367666(n),n=0..70) ; # R. J. Mathar, Dec 04 2023
  • 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-2)\3, v[j+1]*v[i-1-3*j])); v;

Formula

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

A367693 G.f. A(x) satisfies A(x) = 1 / ((1 + x) * (1 - x * A(x^3))).

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, 1, 2, 2, 3, 3, 4, 5, 7, 9, 12, 15, 19, 24, 31, 40, 53, 68, 88, 113, 145, 186, 241, 311, 402, 519, 669, 861, 1110, 1431, 1846, 2382, 3073, 3962, 5109, 6586, 8492, 10952, 14125, 18216, 23493, 30294, 39063, 50373, 64959, 83769, 108030, 139314
Offset: 0

Views

Author

Seiichi Manyama, Nov 27 2023

Keywords

Crossrefs

Cf. A005043, A351973, A367694.
Cf. A367659, A367691.

Programs

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

Formula

a(n) = (-1)^n + Sum_{k=0..floor((n-1)/3)} a(k) * a(n-1-3*k).

A367667 G.f. A(x) satisfies A(x) = 1 / (1 - x - x^3 * A(x^3)).

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 7, 11, 16, 26, 41, 62, 99, 156, 240, 379, 596, 925, 1453, 2281, 3556, 5575, 8742, 13658, 21394, 33524, 52432, 82100, 128597, 201233, 315058, 493377, 772247, 1209008, 1893055, 2963414, 4639389, 7263831, 11371536, 17802783, 27872601, 43635714
Offset: 0

Views

Author

Seiichi Manyama, Nov 26 2023

Keywords

Crossrefs

Cf. A367659, A367666.
Cf. A218032.

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-3)\3, v[j+1]*v[i-2-3*j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-3)/3)} a(k) * a(n-3-3*k).
Showing 1-8 of 8 results.

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