A039909 -id:A039909 - cp's OEIS frontend

A179998 Numbers which are members of both A000140 and A039909.

1, 2, 101, 573, 3836, 29228, 250749, 2409581, 3727542188, 50626553988, 738680521142, 11501573822788, 190418421447330, 3344822488498265, 24965661442811799655, 538134522243713149122, 12140037056605135928410

Offset: 1

Paul Muljadi, Jan 13 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..97

PS:=PowerSeriesRing(Integers()); { Max(Coefficients(&*[&+[ x^i: i in [0..j] ]: j in [0..n-1] ])): n in [1..25] } meet { Max(Coefficients(&*[&+[ (-x)^i: i in [0..j] ]: j in [0..n] ])): n in [1..24] }; // Klaus Brockhaus, Jan 18 2011

A039830 Number of different coefficient values in expansion of Product_{i=1..n} (1-q^1+q^2-...+(-q)^i).

Original entry on oeis.org

1, 2, 4, 4, 6, 16, 22, 15, 19, 46, 56, 34, 40, 92, 106, 61, 69, 154, 172, 96, 106, 232, 254, 139, 151, 326, 352, 190, 204, 436, 466, 249, 265, 562, 596, 316, 334, 704, 742, 391, 411, 862, 904, 474, 496, 1036, 1082, 565, 589, 1226, 1276, 664, 690, 1432, 1486, 771

Offset: 0

Olivier Gérard

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..200

Cf. A039823, A039909.

a(0)=1 prepended by Seiichi Manyama, Jan 05 2023

A369773 Maximal coefficient of (1 + x) * (1 + x - x^2) * ... * (1 + x - x^2 + ... - (-x)^n).

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 19, 59, 233, 1189, 7046, 45326, 356517, 3108808, 30028121, 325635647, 3830546752, 49403859787, 685063715374, 10162709827329, 162776892315940, 2754021620252692, 49463507801582609, 940216720983170113, 18786988751008626812

Offset: 0

Ilya Gutkovskiy, Jan 31 2024

nonn

Cf. A000140, A039828, A039909, A369705, A369774.

Table[Max[CoefficientList[Product[(1 - Sum[(-x)^j, {j, 1, i}]), {i, 1, n}], x]], {n, 0, 24}]

from collections import Counter
def A369773(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            for i in range(1,k+1):
                d[j+i] += (a if i&1 else -a)
        c = d
    return max(c.values()) # Chai Wah Wu, Feb 01 2024

A369774 Maximal coefficient of (1 - x) * (1 - x - x^2) * ... * (1 - x - x^2 - ... - x^n).

Original entry on oeis.org

1, 1, 1, 2, 3, 8, 13, 63, 167, 1227, 5240, 46958, 297080, 3108808, 26714243, 325635647, 3535022425, 49403859787, 646713449897, 10221697892707, 156049674957354, 2756431502525358, 48028121269507891, 940216720983170113, 18359095114316009613

Offset: 0

Ilya Gutkovskiy, Jan 31 2024

nonn

Cf. A000140, A039909, A086376, A369773.

Table[Max[CoefficientList[Product[(1 - Sum[x^j, {j, 1, i}]), {i, 1, n}], x]], {n, 0, 24}]

a(n) = vecmax(Vec(prod(k=1, n, 1 - sum(i=1, k, x^i)))); \\ Michel Marcus, Feb 01 2024

from collections import Counter
def A369774(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            for i in range(1,k+1):
                d[j+i] -= a
        c = d
    return max(c.values()) # Chai Wah Wu, Feb 01 2024

cp's OEIS Frontend

A179998 Numbers which are members of both A000140 and A039909.

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Magma

A039830 Number of different coefficient values in expansion of Product_{i=1..n} (1-q^1+q^2-...+(-q)^i).

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A369773 Maximal coefficient of (1 + x) * (1 + x - x^2) * ... * (1 + x - x^2 + ... - (-x)^n).

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Python

A369774 Maximal coefficient of (1 - x) * (1 - x - x^2) * ... * (1 - x - x^2 - ... - x^n).

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Mathematica

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Python