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.

A369711 Maximum coefficient of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

Original entry on oeis.org

1, 3, 8, 15, 44, 50, 117, 186, 356, 561, 969, 1761, 3508, 5789, 10347, 19023, 35580, 62388, 111255, 205653, 376496, 674085, 1201809, 2211462, 4056220, 7287672, 13027698, 24005627, 43800562, 79033269, 141583272, 260061408, 473603594, 855436899, 1532383878, 2813222766
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 29 2024

Keywords

Crossrefs

Cf. A010816, A086376, A369709.

Programs

  • Mathematica
    Table[Max[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]], {n, 0, 35}]
  • PARI
    a(n) = vecmax(Vec(prod(i=1, n, (1-x^i)^3))); \\ Michel Marcus, Jan 29 2024
  • Python
    from collections import Counter
def A369711(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            d[j+k] -= 3*a
            d[j+2*k] += 3*a
            d[j+3*k] -= a
        c = d
    return max(c.values()) # Chai Wah Wu, Feb 07 2024

A369983 Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

Original entry on oeis.org

1, 3, 8, 15, 44, 50, 117, 186, 356, 561, 972, 1761, 3508, 5789, 10470, 19023, 35580, 62388, 113418, 205653, 376496, 674085, 1226181, 2211462, 4056220, 7287672, 13261764, 24005627, 43800562, 79033269, 143513301, 260061408, 473603594, 855436899, 1553736558, 2813222766
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 07 2024

Keywords

Crossrefs

Cf. A010816, A133871, A160089, A369709, A369711, A369790.

Programs

  • Mathematica
    Table[Max[Abs[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]]], {n, 0, 35}]
  • PARI
    a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^i)^3)))); \\ Michel Marcus, Feb 07 2024
  • Python
    from collections import Counter
def A369983(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            d[j+k] -= 3*a
            d[j+2*k] += 3*a
            d[j+3*k] -= a
        c = d
    return max(map(abs,c.values())) # Chai Wah Wu, Feb 07 2024

A369725 Maximal coefficient of ( (1 + x) * (1 + x^2) * (1 + x^3) * ... * (1 + x^n) )^n.

Original entry on oeis.org

1, 1, 4, 62, 4658, 1585430, 2319512420, 14225426190522, 361926393013029354, 37883831957216781279561, 16231015449888734994721650504, 28330316118212024049511095643949434, 200866780133770636272812495083578779133456, 5771133366532656054669819186294860881172794669798
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 30 2024

Keywords

Crossrefs

Cf. A025591, A047653, A270913, A369709.

Programs

  • Maple
    a:= n-> max(coeffs(expand(mul(1+x^k, k=1..n)^n))):
seq(a(n), n=0..14);  # Alois P. Heinz, Jan 30 2024
  • Mathematica
    Table[Max[CoefficientList[Product[(1 + x^k)^n, {k, 1, n}], x]], {n, 0, 13}]
  • PARI
    a(n) = vecmax(Vec(prod(k=1, n, (1+x^k))^n)); \\ Michel Marcus, Jan 30 2024

A380517 Absolute value of the minimum coefficient of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

Original entry on oeis.org

1, 3, 6, 15, 24, 50, 81, 186, 305, 561, 972, 1761, 3129, 5789, 10470, 19023, 33549, 62388, 113418, 205653, 366198, 674085, 1226181, 2211462, 3953679, 7287672, 13261764, 24005627, 42998125, 79033269, 143513301, 260061408, 465444889, 855436899, 1553736558, 2813222766, 5052061560, 9250734231
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 26 2025

Keywords

Crossrefs

Cf. A010816, A086394, A369709, A369711, A369983, A380499.

Programs

  • Maple
    p:= proc(n) option remember;
     `if`(n=0, 1, expand(p(n-1)*(1-x^n)^3))
    end:
a:= n-> abs(min(coeffs(p(n)))):
seq(a(n), n=0..37);  # Alois P. Heinz, Jan 26 2025
  • Mathematica
    Table[Min[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]], {n, 0, 37}] // Abs
  • PARI
    a(n) = abs(vecmin(Vec(prod(k=1, n, (1-x^k)^3)))); \\ Michel Marcus, Jan 26 2025
Showing 1-4 of 4 results.

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