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A193513
Number of partitions of n into parts having at least one common digit in decimal representation.
2
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
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
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