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A261131 Number of ways to write n as the sum of 3 positive palindromes. 6
0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 13, 15, 14, 15, 14, 14, 12, 12, 9, 9, 8, 7, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Conjecture: a(n) > 0 for n > 2, i.e., every number greater than 2 can be written as the sum of 3 positive palindromes.

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..10000

EXAMPLE

a(28) = 5 since 28 can be expressed in 5 ways as the sum of 3 positive palindromes, namely, 28 = 22+5+1 = 22+4+2 = 22+3+3 = 11+11+6 = 11+9+8.

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, t) option remember; `if`(n=0, 1, `if`(i<1 or

      t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))

    end:

a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(3):

seq(a(n), n=0..120);  # Alois P. Heinz, Sep 19 2018

MATHEMATICA

pal=Select[Range@ 1000, (d = IntegerDigits@ #; d == Reverse@ d)&]; a[n_] := Length@ IntegerPartitions[n, {3}, pal]; a /@ Range[0, 1000]

CROSSREFS

Cf. A002113, A260254, A261132.

Column k=3 of A319453.

Sequence in context: A047503 A228803 A037014 * A225061 A133223 A065003

Adjacent sequences:  A261128 A261129 A261130 * A261132 A261133 A261134

KEYWORD

nonn,base,look

AUTHOR

Giovanni Resta, Aug 10 2015

STATUS

approved

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Last modified October 22 11:13 EDT 2018. Contains 316438 sequences. (Running on oeis4.)