A179051 Number of partitions of n into powers of 10 (cf. A011557).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

0,11

Comments

A179052 and A008592 give record values and where they occur.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for related partition-counting sequences

Formula

a(n) = A133880(n) for n < 90; a(n) = A132272(n) for n < 100.

a(10^n) = A145513(n).

a(10*n) = A179052(n).

A179052(n) = a(A008592(n));

a(n) = p(n,1) where p(n,k) = if k<=n then p(10*[(n-k)/10],k)+p(n,10*k) else 0^n.

G.f.: Product_{k>=0} 1/(1 - x^(10^k)). - Ilya Gutkovskiy, Jul 26 2017

Example

a(19) = #{10 + 9x1, 19x1} = 2;
a(20) = #{10 + 10, 10 + 10x1, 20x1} = 3;
a(21) = #{10 + 10 + 1, 10 + 11x1, 21x1} = 3.

Mathematica

terms = 10001;
CoefficientList[Product[1/(1 - x^(10^k)) + O[x]^terms,
     {k, 0, Log[10, terms] // Ceiling}], x]
(* Jean-François Alcover, Dec 12 2021, after Ilya Gutkovskiy *)

Prog

(Haskell)
a179051 = p 1 where
   p _ 0 = 1
   p k m = if m < k then 0 else p k (m - k) + p (k * 10) m
-- Reinhard Zumkeller, Feb 05 2012

Crossrefs

Number of partitions of n into powers of b: A018819 (b=2), A062051 (b=3).

Cf. A206245, A000041, A179051.

Cf. A133880, A132272.

Cf. A008592, A179052.

Sequence in context: A329624 A059995 A132272 * A324160 A054899 A061217

Adjacent sequences: A179048 A179049 A179050 * A179052 A179053 A179054

Keyword

nonn

Author

Reinhard Zumkeller, Jun 27 2010

Status

approved