A341168 -id:A341168 - cp's OEIS frontend

A341207 Number of ways to write n as an ordered sum of 10 nonzero decimal palindromes.

1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48610, 92288, 167500, 292180, 491920, 802120, 1270324, 1958605, 2945800, 4329370, 6226580, 8774695, 12129890, 16464610, 21963190, 28815655, 37209766, 47321560, 59304730, 73279565, 89322100, 107454362, 127636600, 149762345, 173657020

Offset: 10

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 10..10000

Cf. A002113, A136522, A319475, A341168, A341184, A341191, A341192, A341193, A341203, A341204, A341205, A341206.

nmax = 43; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

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

A341167 Number of partitions of n into 9 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 12, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 14, 15, 16, 16, 17, 17, 19, 19, 21, 22, 24, 22, 25, 25, 26, 26, 26, 27

Offset: 45

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 45..20000

Cf. A002113, A136522, A319474, A341155, A341156, A341157, A341158, A341159, A341165, A341166, A341168.

cp's OEIS Frontend

A341207 Number of ways to write n as an ordered sum of 10 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

A341167 Number of partitions of n into 9 distinct nonzero decimal palindromes.

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