A341167 -id:A341167 - cp's OEIS frontend

A341206 Number of ways to write n as an ordered sum of 9 nonzero decimal palindromes.

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24301, 43686, 75249, 124809, 200115, 311157, 470415, 693000, 996633, 1401436, 1929465, 2603979, 3448440, 4485267, 5734395, 7211718, 8927523, 10885050, 13079257, 15496065, 18112050, 20894757, 23803659, 26791749, 29807697, 32798448

Offset: 9

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 9..10000

Cf. A002113, A136522, A319474, A341167, A341184, A341191, A341192, A341193, A341203, A341204, A341205, A341207.

p:= proc(n) option remember; local i, s; s:= ""||n;
      for i to iquo(length(s), 2) do if
        s[i]<>s[-i] then return false fi od; true
    end:
b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(t<1, 0, add(`if`(p(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..43);  # Alois P. Heinz, Feb 07 2021

nmax = 43; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

A341165 Number of partitions of n into 7 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 6, 7, 8, 8, 10, 9, 10, 9, 9, 8, 8, 7, 7, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 18, 19, 19, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 21, 21, 22, 24, 25, 28, 29, 32, 33, 36, 37, 40, 39, 41, 41, 42, 42, 42, 42, 42, 42, 43, 44, 43, 45, 47, 48

Offset: 28

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 28..20000

Cf. A002113, A136522, A319472, A341155, A341156, A341157, A341158, A341159, A341166, A341167, A341168.

p:= proc(n) option remember; local i, s; s:= ""||n;
      for i to iquo(length(s), 2) do if
        s[i]<>s[-i] then return false fi od; true
    end:
h:= proc(n) option remember; `if`(n<1, 0,
     `if`(p(n), n, h(n-1)))
    end:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i (k-> b(n, h(n), k)-b(n, h(n), k-1))(7):
seq(a(n), n=28..97);  # Alois P. Heinz, Feb 06 2021

A341166 Number of partitions of n into 8 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 6, 7, 8, 8, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 10, 11, 11, 11, 11, 11, 12, 12, 13, 14, 15, 16, 19, 20, 22, 24, 25, 27, 28, 29, 29, 30, 29, 31, 30, 30, 30, 30, 31, 31, 32, 33, 34, 35, 39, 39

Offset: 36

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 36..20000

Cf. A002113, A136522, A319473, A341155, A341156, A341157, A341158, A341159, A341165, A341167, A341168.

p:= proc(n) option remember; local i, s; s:= ""||n;
      for i to iquo(length(s), 2) do if
        s[i]<>s[-i] then return false fi od; true
    end:
h:= proc(n) option remember; `if`(n<1, 0,
     `if`(p(n), n, h(n-1)))
    end:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i (k-> b(n, h(n), k)-b(n, h(n), k-1))(8):
seq(a(n), n=36..105);  # Alois P. Heinz, Feb 06 2021

A341168 Number of partitions of n into 10 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 4, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 7, 6, 6, 7, 7, 8, 8, 9, 9, 9, 8, 11, 9, 9, 10, 10, 11, 11

Offset: 56

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 56..20000

Cf. A002113, A136522, A319475, A341155, A341156, A341157, A341158, A341159, A341165, A341166, A341167.

cp's OEIS Frontend

A341206 Number of ways to write n as an ordered sum of 9 nonzero decimal palindromes.

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A341165 Number of partitions of n into 7 distinct nonzero decimal palindromes.

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A341166 Number of partitions of n into 8 distinct nonzero decimal palindromes.

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Maple

A341168 Number of partitions of n into 10 distinct nonzero decimal palindromes.

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