A260254 Number of ways to write n as sum of two palindromes in decimal representation.

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 0, 4, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Reinhard Zumkeller, Jul 21 2015

Keywords

• nonn
• base
• look

Comments

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

Examples

			.   n | a(n) |                                n | a(n) |
. ----+------+--------------------------    ----+------+--------------
.   0 |    1 |  0                            21 |    0 |  ./.
.   1 |    1 |  1                            22 |    2 |  22, 11+11
.   2 |    2 |  2, 1+1                       23 |    1 |  22+1
.   3 |    2 |  3, 2+1                       24 |    1 |  22+2
.   4 |    3 |  4, 3+1, 2+2                  25 |    1 |  22+3
.   5 |    3 |  5, 4+1, 3+2                  26 |    1 |  22+4
.   6 |    4 |  6, 5+1, 4+2, 3+3             27 |    1 |  22+5
.   7 |    4 |  7, 6+1, 5+2, 4+3             28 |    1 |  22+6
.   8 |    5 |  8, 7+1, 6+2, 5+3, 4+4        29 |    1 |  22+7
.   9 |    5 |  9, 8+1, 7+2, 6+3, 5+4        30 |    1 |  22+8
.  10 |    5 |  9+1, 8+2, 7+3, 6+4, 5+5      31 |    1 |  22+9
.  11 |    5 |  11, 9+2, 8+3, 7+4, 6+5       32 |    0 |  ./.
.  12 |    5 |  11+1, 9+3, 8+4, 7+5, 6+6     33 |    2 |  33, 22+11
.  13 |    4 |  11+2, 9+4, 8+5, 7+6          34 |    1 |  33+1
.  14 |    4 |  11+3, 9+5, 8+6, 7+7          35 |    1 |  33+2
.  15 |    3 |  11+4, 9+6, 8+7               36 |    1 |  33+3
.  16 |    3 |  11+5, 9+7, 8+8               37 |    1 |  33+4
.  17 |    2 |  11+6, 9+8                    38 |    1 |  33+5
.  18 |    2 |  11+7, 9+9                    39 |    1 |  33+6
.  19 |    1 |  11+8                         40 |    1 |  33+7
.  20 |    1 |  11+9                         41 |    1 |  33+8  .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Hugo Pfoertner, Plot of first 10^6 terms
• Hugo Pfoertner, Plot of first 3*10^7 terms

Crossrefs

Cf. A002113, A136522, A035137, A260255.

Programs

Haskell

a260254 n = sum $ map (a136522 . (n -)) $
               takeWhile (<= n `div` 2) a002113_list

Formula

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