%I #23 Aug 15 2015 08:04:18

%S 1,1,2,2,3,3,4,4,5,5,5,5,5,4,4,3,3,2,2,1,1,0,2,1,1,1,1,1,1,1,1,1,0,2,

%T 1,1,1,1,1,1,1,1,1,0,3,1,1,1,1,1,1,1,1,1,0,3,1,1,1,1,1,1,1,1,1,0,4,1,

%U 1,1,1,1,1,1,1,1,0,4,1,1,1,1,1,1,1,1

%N Number of ways to write n as sum of two palindromes in decimal representation.

%C a(A035137(n)) = 0; a(A260255(n)) > 0.

%H Reinhard Zumkeller, <a href="/A260254/b260254.txt">Table of n, a(n) for n = 0..10000</a>

%H Hugo Pfoertner, <a href="/A260254/a260254_2.png">Plot of first 10^6 terms</a>

%H Hugo Pfoertner, <a href="/A260254/a260254_1.png">Plot of first 3*10^7 terms</a>

%F a(n) = sum{A136522(n - A002113(k)): k = 1..floor(n/2)}.

%e . n | a(n) | n | a(n) |

%e . ----+------+-------------------------- ----+------+--------------

%e . 0 | 1 | 0 21 | 0 | ./.

%e . 1 | 1 | 1 22 | 2 | 22, 11+11

%e . 2 | 2 | 2, 1+1 23 | 1 | 22+1

%e . 3 | 2 | 3, 2+1 24 | 1 | 22+2

%e . 4 | 3 | 4, 3+1, 2+2 25 | 1 | 22+3

%e . 5 | 3 | 5, 4+1, 3+2 26 | 1 | 22+4

%e . 6 | 4 | 6, 5+1, 4+2, 3+3 27 | 1 | 22+5

%e . 7 | 4 | 7, 6+1, 5+2, 4+3 28 | 1 | 22+6

%e . 8 | 5 | 8, 7+1, 6+2, 5+3, 4+4 29 | 1 | 22+7

%e . 9 | 5 | 9, 8+1, 7+2, 6+3, 5+4 30 | 1 | 22+8

%e . 10 | 5 | 9+1, 8+2, 7+3, 6+4, 5+5 31 | 1 | 22+9

%e . 11 | 5 | 11, 9+2, 8+3, 7+4, 6+5 32 | 0 | ./.

%e . 12 | 5 | 11+1, 9+3, 8+4, 7+5, 6+6 33 | 2 | 33, 22+11

%e . 13 | 4 | 11+2, 9+4, 8+5, 7+6 34 | 1 | 33+1

%e . 14 | 4 | 11+3, 9+5, 8+6, 7+7 35 | 1 | 33+2

%e . 15 | 3 | 11+4, 9+6, 8+7 36 | 1 | 33+3

%e . 16 | 3 | 11+5, 9+7, 8+8 37 | 1 | 33+4

%e . 17 | 2 | 11+6, 9+8 38 | 1 | 33+5

%e . 18 | 2 | 11+7, 9+9 39 | 1 | 33+6

%e . 19 | 1 | 11+8 40 | 1 | 33+7

%e . 20 | 1 | 11+9 41 | 1 | 33+8 .

%o (Haskell)

%o a260254 n = sum $ map (a136522 . (n -)) $

%o takeWhile (<= n `div` 2) a002113_list

%Y Cf. A002113, A136522, A035137, A260255.

%K nonn,base,look

%O 0,3

%A _Reinhard Zumkeller_, Jul 21 2015