cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A091580 Number of partitions of n into decimal palindromes.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 74, 96, 126, 162, 208, 263, 333, 415, 518, 639, 788, 962, 1174, 1420, 1716, 2060, 2468, 2940, 3497, 4137, 4886, 5747, 6744, 7885, 9203, 10702, 12424, 14379, 16611, 19136, 22009, 25245, 28915, 33037, 37688, 42901, 48765
Offset: 0

Views

Author

Reinhard Zumkeller, Jan 22 2004

Keywords

Examples

			n=12: there are A000041(12)=77 partitions of 12, 3 of them contain non-palindromes: 12=10+2, 12=10+1+1 and 12 itself, therefore a(12)=77-3=74.

Links

Crossrefs

Cf. A002113, A091581.
Different from A088669 and from A000041.
Row sums of A319453.

Programs

  • Maple
    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) option remember; `if`(n=0 or i=1, 1,
      b(n, h(i-1))+b(n-i, h(min(n-i, i))))
    end:
a:= n-> b(n, h(n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Sep 19 2018

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 17 2018

A088670 Number of partitions of n into distinct decimal repdigit numbers.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 17, 19, 21, 23, 26, 27, 30, 32, 34, 36, 37, 39, 40, 42, 42, 44, 44, 45, 45, 47, 47, 47, 49, 48, 50, 50, 52, 52, 55, 55, 58, 60, 60, 64, 65, 68, 69, 73, 73, 77, 78, 82, 84, 84, 88, 88, 92, 92, 96, 96, 100, 100, 105, 107, 107, 113
Offset: 0

Views

Author

Reinhard Zumkeller, Oct 03 2003

Keywords

Comments

a(n) <= A000009(n).
Not the same as A091581: a(n) < A091581(n) for n > 101.
A109967(n) = a(n+1) - a(n). - Reinhard Zumkeller, Jul 06 2005

Links

Crossrefs

Cf. A010785, A088669, A109968, A131364.

Programs

  • Haskell
    a088670 = p $ tail a010785_list where
   p _      0 = 1
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
-- Reinhard Zumkeller, Dec 10 2011

Extensions

a(0)=1 added and offset adjusted by Reinhard Zumkeller, Dec 10 2011

A109968 Number of partitions of n into decimal repdigits of distinct digits.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 18, 20, 21, 24, 24, 27, 27, 30, 30, 30, 31, 32, 32, 31, 32, 31, 32, 29, 31, 29, 30, 28, 28, 28, 27, 29, 27, 28, 26, 30, 28, 30, 29, 30, 30, 31, 31, 32, 35, 31, 38, 33, 35, 34, 36, 38, 39, 38, 37, 39, 38, 43, 40, 44, 42, 44, 43, 44, 44
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 06 2005

Keywords

Comments

a(n) <= A109950(n) <= A000009(n);
A109969(n) = a(n+1) - a(n);
all partitions have no more than 9 parts.

Examples

			a(60)=38: 60 = 55+4+1 = 55+3+2 = 44+11+5 = 44+11+3+2 =
44+9+7 = 44+9+6+1 = 44+9+5+2 = 44+8+7+1 = 44+8+6+2 =
44+8+5+3 = 44+8+5+2+1 = 44+7+6+3 = 44+7+6+2+1 = 44+7+5+3+1 =
44+6+5+3+2 = 33+22+5 = 33+22+4+1 = 33+11+9+7 = 33+11+9+5+2 =
33+11+8+6+2 = 33+11+7+5+4 = 33+9+8+7+2+1 = 33+9+8+6+4 =
33+9+8+5+4+1 = 33+9+7+6+5 = 33+9+7+6+4+1 = 33+9+7+5+4+2 =
33+9+6+5+4+2+1 = 33+8+7+6+5+1 = 33+8+7+6+4+2 =
33+8+7+5+4+2+1 = 22+11+9+8+7+3 = 22+11+9+8+6+4 =
22+11+9+7+6+5 = 22+11+9+6+5+4+3 = 22+11+8+7+5+4+3 =
22+9+8+7+6+5+3 = 22+9+8+7+6+4+3+1.

Links

Crossrefs

Cf. A088670, A088669, A010785.

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 18 2016

A131361 Number of partitions of n into repdigits of digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 8, 6, 5, 5, 4, 4, 4, 4, 1, 17, 2, 4, 8, 3, 6, 2, 5, 2, 1, 22, 8, 2, 3, 3, 8, 2, 2, 6, 1, 27, 17, 5, 2, 3, 4, 2, 8, 2, 1, 32, 11, 6, 4, 2, 2, 2, 2, 2, 1, 37, 22, 17, 8, 4, 2, 2, 3, 4, 1, 42, 14, 7, 4, 4, 2, 2, 2, 2, 1, 47, 27, 7, 17, 4, 5, 2, 2, 2, 1, 52, 16, 22, 4, 4, 8, 2
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 03 2007

Keywords

Comments

See A131362 and A131363 for record values and where they occur.

Examples

			a(10) = #{1+1+1+1+1+1+1+1+1+1} = 1;
a(11) = #{11, 1+1+1+1+1+1+1+1+1+1+1} = 2;
a(12) = #{11+1, 2+2+2+2+2+2, 2+2+2+2+2+1+1, 2+2+2+2+1+1+1+1, 2+2+2+1+1+1+1+1+1, 2+2+1+1+1+1+1+1+1+1, 2+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1} = 8;
a(13) = #{11+1+1, 3+3+3+3+1, 3+3+3+1+1+1+1, 3+3+1+1+1+1+1+1+1, 3+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1} = 6;
a(14) = #{11+1+1+1, 4+4+4+1+1, 4+4+1+1+1+1+1+1, 4+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1+1} = 5;
a(15) = #{11+1+1+1+1, 5+5+5, 5+5+1+1+1+1+1, 5+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1} = 5;
a(16) = #{11+1+1+1+1+1, 6+6+1+1+1+1, 6+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1} = 4;
a(17) = #{11+1+1+1+1+1+1, 7+7+1+1+1, 7+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1} = 4;
a(18) = #{11+1+1+1+1+1+1+1, 8+8+1+1, 8+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1} = 4;
a(19) = #{11+1+1+1+1+1+1+1+1, 9+9+1, 9+1+1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1} = 4.

Links

Crossrefs

Cf. A000929 (binary analog), A131362, A131363, A131364, A088669.

Programs

  • Haskell
    a131361 n = p [r | r <- tail a010785_list, head (show r) `elem` show n] n
   where p _          0 = 1
         p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Dec 10 2011

Extensions

a(0)=1 added and offset adjusted by Reinhard Zumkeller, Dec 10 2011
Showing 1-4 of 4 results.

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