A329257 -id:A329257 - cp's OEIS frontend

A329310 a(n) is the sum of the numbers k such that a(n-2k) = a(n-k) and 0 < n-2k < n-k < n.

0, 0, 1, 0, 0, 3, 3, 4, 4, 1, 0, 0, 1, 0, 0, 6, 16, 10, 11, 17, 10, 10, 31, 13, 10, 27, 13, 16, 18, 3, 0, 7, 0, 0, 3, 0, 3, 2, 16, 5, 5, 1, 0, 7, 0, 0, 19, 17, 3, 37, 38, 28, 52, 74, 34, 55, 82, 61, 27, 53, 132, 29, 71, 90, 32, 32, 95, 82, 0, 34, 92, 29, 0, 63

Offset: 1

Rémy Sigrist, Nov 10 2019

nonn

			The first terms, alongside the corresponding k's, are:
  n    a(n)  k's
  ---  ----  ---------
    1     0  {}
    2     0  {}
    3     1  {1}
    4     0  {}
    5     0  {}
    6     3  {1, 2}
    7     3  {3}
    8     4  {1, 3}
    9     4  {4}
   10     1  {1}
   11     0  {}
   12     0  {}
   13     1  {1}
   14     0  {}
   15     0  {}
   16     6  {1, 2, 3}
   17    16  {3, 6, 7}

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A329310
Rémy Sigrist, Scatterplot of the first 500000 terms

See A329257 for similar sequences.

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A329311 a(n) is the product of the numbers k such that a(n-2k) = a(n-k) and 0 < n-2k < n-k < n.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 8, 10, 90, 42, 42, 56, 56, 72, 9, 10, 1, 1, 1, 1, 2, 2, 3, 8, 1, 1, 1, 11, 24, 780, 1092, 7644, 11760, 11760, 311040, 2736, 64600, 420, 420, 462, 157080, 10626, 483, 210672, 20, 420, 462, 462, 506, 23, 624, 27, 5292, 45472, 812

Offset: 1

Rémy Sigrist, Nov 10 2019

This sequence has fractal features; apparently, for any k > 0, the first k terms are repeated later (see illustration in Links section).

			The first terms, alongside the corresponding k's, are:
  n    a(n)     k's
  ---  -------  ---------
    1        1  {}
    2        1  {}
    3        1  {1}
    4        1  {1}
    5        2  {1, 2}
    6        2  {2}
    7        3  {1, 3}
    8        1  {}
    9        1  {}
   10        1  {1}
   11        1  {1}
   12        8  {1, 2, 4}
   13       10  {2, 5}
   14       90  {3, 5, 6}
   15       42  {6, 7}
   16       42  {6, 7}
   17       56  {1, 7, 8}

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Logarithmic scatterplot of the first 80000 terms (the two colored sections are equal up to an horizontal shift)

See A329257 for similar sequences.

for (n=1, #(a=vector(60)), print1 (a[n] = prod(k=1, (n-1)\2, if (a[n-k]==a[n-2*k], k, 1)) ", "))

cp's OEIS Frontend

A329310 a(n) is the sum of the numbers k such that a(n-2k) = a(n-k) and 0 < n-2k < n-k < n.

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A329311 a(n) is the product of the numbers k such that a(n-2k) = a(n-k) and 0 < n-2k < n-k < n.

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cp's OEIS Frontend

A329310 a(n) is the sum of the numbers k such that a(n-2*k) = a(n-k) and 0 < n-2*k < n-k < n.

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C

A329311 a(n) is the product of the numbers k such that a(n-2*k) = a(n-k) and 0 < n-2*k < n-k < n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A329310 a(n) is the sum of the numbers k such that a(n-2k) = a(n-k) and 0 < n-2k < n-k < n.

A329311 a(n) is the product of the numbers k such that a(n-2k) = a(n-k) and 0 < n-2k < n-k < n.