A193513 - OEIS

%I #15 Jun 01 2024 09:57:10

%S 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,

%T 51,49,64,62,79,77,95,101,118,118,143,145,179,181,216,223,267,286,325,

%U 341,399,416,485,500,575,600,686,735,823,864,981,1032,1180

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

%e a(7) = #{7, 7x1} = 2;

%e a(8) = #{8, 4+4, 2+2+2+2, 8x1} = 4;

%e a(9) = #{9, 3+3+3, 9x1} = 3;

%e a(10) = #{10, 5+5, 2+2+2+2+2, 10x1} = 4;

%e a(11) = #{11, 10+1, 11x1} = 3;

%e a(12) = #{12, 11+1, 10+1+1, 6+6, 4+4+4, 3+3+3+3, 6x2, 10x1} = 8;

%e a(13) = #{13, 12+1, 11+1+1, 10+1+1+1, 13x1} = 5;

%e a(14) = #{14, 13+1, 12+2, 12+1+1, 11+1+1+1, 10+4x1, 7+7, 7x2, 14x1} = 9.

%o (Haskell)

%o import Data.List (intersect)

%o a193513 n = p "0123456789" n 1 where

%o    p "" _ _      = 0

%o    p _  0 _      = 1

%o    p cds m k

%o      | m < k     = 0

%o      | otherwise = p (cds `intersect` show k) (m - k) k + p cds m (k + 1)

%Y Cf. A061827, A061828, A109950, A119999.

%K nonn,base

%O 0,3

%A _Reinhard Zumkeller_, Jul 30 2011

%E Thanks to Douglas McNeil, who noticed a program error; data corrected and program fixed by _Reinhard Zumkeller_, Aug 01 2011