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A261131
Number of ways to write n as the sum of 3 positive palindromes.
8
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
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
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]
Table[Count[IntegerPartitions[n, {3}], _?(AllTrue[#, PalindromeQ]&)], {n, 0, 90}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 26 2021 *)
CROSSREFS
Column k=3 of A319453.
Sequence in context: A047503 A228803 A037014 * A225061 A133223 A065003
KEYWORD
nonn,base,look
AUTHOR
Giovanni Resta, Aug 10 2015
STATUS
approved