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

Author

Reinhard Zumkeller, Jul 30 2011

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

Cf. A061827, A061828, A109950, A119999.

Programs

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)

Extensions

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