A114102 Number of partitions of n such that all parts of a partition have the same digital root.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 3, 7, 4, 5, 7, 6, 5, 8, 5, 8, 11, 8, 7, 16, 9, 10, 13, 12, 10, 22, 11, 15, 23, 16, 16, 26, 16, 18, 32, 22, 21, 41, 24, 27, 40, 28, 26, 55, 30, 36, 59, 40, 38, 65, 41, 45, 77, 48, 51, 95, 57, 60, 97, 66, 63, 119, 68, 80, 131, 89, 85, 150, 91, 96, 166, 104

Offset

1,2

Comments

a(n) = A116371(n) + A116372(n) + A116373(n) + A116374(n) + A116375(n) + A116376(n) + A116377(n) + A116378(n) + A114099(n).

Links

Table of n, a(n) for n=1..76.

Eric Weisstein's World of Mathematics, Digital Root

Example

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

Prog

(Haskell)
a114102 n = length $ filter (== 1) $
            map (length . nub . (map a010888)) $ ps 1 n
   where ps x 0 = [[]]
         ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)]
-- Reinhard Zumkeller, Feb 04 2014

Crossrefs

Cf. A010888.

A147706. [From Reinhard Zumkeller, Nov 11 2008]

A156144. [From Reinhard Zumkeller, Feb 05 2009]

Sequence in context: A368195 A218705 A193459 * A193513 A218704 A144373

Adjacent sequences: A114099 A114100 A114101 * A114103 A114104 A114105

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 12 2006

Status

approved