A341155 -id:A341155 - cp's OEIS frontend

A341156 Number of partitions of n into 3 distinct nonzero decimal palindromes.

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

Offset: 6

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 6..20000

Cf. A002113, A136522, A261131, A261132, A261422, A341155, A341157, A341158, A341159.

A341157 Number of partitions of n into 4 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 8, 10, 12, 13, 15, 15, 16, 16, 15, 14, 13, 11, 10, 9, 8, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 11, 11, 11, 11, 11, 12, 12, 13, 13, 14, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 16, 15, 15, 15, 15, 16

Offset: 10

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 10..20000

Cf. A002113, A136522, A319469, A341155, A341156, A341158, A341159.

A341158 Number of partitions of n into 5 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 9, 10, 13, 14, 17, 17, 19, 18, 19, 17, 17, 15, 14, 12, 12, 11, 11, 11, 12, 13, 14, 15, 16, 17, 18, 18, 19, 19, 19, 19, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 21, 21, 22, 23, 24, 26, 26, 28, 28, 29, 29, 31, 29, 30, 30, 30, 30, 30, 30, 30, 30, 31

Offset: 15

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 15..20000

Cf. A002113, A136522, A319470, A341155, A341156, A341157, A341159.

A341159 Number of partitions of n into 6 distinct nonzero decimal palindromes.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 8, 9, 11, 13, 14, 15, 16, 16, 15, 15, 14, 13, 12, 11, 11, 11, 12, 12, 14, 15, 17, 18, 20, 20, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 22, 23, 23, 23, 24, 24, 25, 26, 28, 29, 31, 32, 35, 36, 38, 39, 40, 41, 41, 42, 42, 42, 41, 43, 42, 42, 43, 43, 44, 45, 47

Offset: 21

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 21..20000

Cf. A002113, A136522, A319471, A341155, A341156, A341157, A341158.

Table[Count[IntegerPartitions[n,{6}],?(Length[Union[#]]==Length[#]&&AllTrue[ #,PalindromeQ]&)],{n,21,100}] (* _Harvey P. Dale, Jul 27 2021 *)

A341191 Number of ways to write n as an ordered sum of 2 nonzero decimal palindromes.

Original entry on oeis.org

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

Offset: 2

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 2..20000

Cf. A002113, A136522, A260254, A319468, A341155, A341192, A341193.

nmax = 90; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^2, {x, 0, nmax}], x] // Drop[#, 2] &

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.

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.

A364836 a(n) is the least positive integer that can be expressed as the sum of two distinct nonzero decimal palindromes in exactly n ways.

Original entry on oeis.org

1, 3, 5, 7, 9, 110, 353, 363, 373, 383, 393, 524, 474, 484, 565, 494, 575, 615, 585, 837, 595, 716, 686, 1342, 777, 696, 1332, 787, 878, 918, 797, 888, 979, 32212, 12892, 898, 989, 1009, 11220, 54544, 999, 30902, 11110, 43423, 42623, 28982, 1100, 11000, 35753, 36663

Offset: 0

Ilya Gutkovskiy, Aug 28 2023

			For n = 5: 110 = 9 + 101 = 11 + 99 = 22 + 88 = 33 + 77 = 44 + 66.

Cf. A002113, A115336, A341155.

a(33) and beyond from Michael S. Branicky, Aug 31 2023

cp's OEIS Frontend

A341156 Number of partitions of n into 3 distinct nonzero decimal palindromes.

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A341157 Number of partitions of n into 4 distinct nonzero decimal palindromes.

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A341158 Number of partitions of n into 5 distinct nonzero decimal palindromes.

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A341159 Number of partitions of n into 6 distinct nonzero decimal palindromes.

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Mathematica

A341191 Number of ways to write n as an ordered sum of 2 nonzero decimal palindromes.

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Mathematica

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

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Maple

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

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A364836 a(n) is the least positive integer that can be expressed as the sum of two distinct nonzero decimal palindromes in exactly n ways.

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