A116371 Number of partitions of n into parts with digital root = 1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 8, 10, 11, 12, 12, 12, 12, 12, 12, 13, 15, 17, 18, 19, 19, 19, 19, 19, 20, 23, 26, 28, 29, 30, 30, 30, 30, 31, 34, 38, 41, 43, 44, 45, 45, 45, 46, 50, 55, 60, 63, 65, 66, 67, 67, 68

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2006

Keywords

• nonn
• base

Comments

a(n) = A114102(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116376(n) - A116377(n) - A116378(n) - A114099(n).

Examples

			a(18) = #{10+8x1, 18x1} = 2;
a(19) = #{19, 10+9x1, 19x1} = 3;
a(20) = #{19+1, 10+10, 10+10x1, 19x1} = 4.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..500
• Eric Weisstein's World of Mathematics, Digital Root

Crossrefs

Cf. A010888.

A147706. [From Reinhard Zumkeller, Nov 11 2008]

A017173, A156144, A156145. [From Reinhard Zumkeller, Feb 05 2009]

Programs

Haskell

a116371 n = p a017173_list n where
   p _  0 = 1
   p [] _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Feb 04 2014