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

0,3

Comments

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

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

Formula

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

Example

.   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  .

Prog

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

Crossrefs

Cf. A002113, A136522, A035137, A260255.

Sequence in context: A262907 A341721 A290323 * A337853 A282711 A035100

Adjacent sequences: A260251 A260252 A260253 * A260255 A260256 A260257

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Jul 21 2015

Status

approved