A193513 Number of partitions of n into parts having at least one common digit in decimal representation.

1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 3, 8, 5, 9, 9, 13, 9, 16, 12, 18, 16, 23, 20, 31, 30, 38, 38, 51, 49, 64, 62, 79, 77, 95, 101, 118, 118, 143, 145, 179, 181, 216, 223, 267, 286, 325, 341, 399, 416, 485, 500, 575, 600, 686, 735, 823, 864, 981, 1032, 1180

Offset

0,3

Links

Table of n, a(n) for n=0..60.

Example

a(7) = #{7, 7x1} = 2;
a(8) = #{8, 4+4, 2+2+2+2, 8x1} = 4;
a(9) = #{9, 3+3+3, 9x1} = 3;
a(10) = #{10, 5+5, 2+2+2+2+2, 10x1} = 4;
a(11) = #{11, 10+1, 11x1} = 3;
a(12) = #{12, 11+1, 10+1+1, 6+6, 4+4+4, 3+3+3+3, 6x2, 10x1} = 8;
a(13) = #{13, 12+1, 11+1+1, 10+1+1+1, 13x1} = 5;
a(14) = #{14, 13+1, 12+2, 12+1+1, 11+1+1+1, 10+4x1, 7+7, 7x2, 14x1} = 9.

Prog

(Haskell)
import Data.List (intersect)
a193513 n = p "0123456789" n 1 where
   p "" _ _      = 0
   p _  0 _      = 1
   p cds m k
     | m < k     = 0
     | otherwise = p (cds `intersect` show k) (m - k) k + p cds m (k + 1)

Crossrefs

Cf. A061827, A061828, A109950, A119999.

Sequence in context: A218705 A193459 A114102 * A218704 A144373 A086292

Adjacent sequences: A193510 A193511 A193512 * A193514 A193515 A193516

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 30 2011

Extensions

Thanks to Douglas McNeil, who noticed a program error; data corrected and program fixed by Reinhard Zumkeller, Aug 01 2011

Status

approved