A179051 - OEIS

%I #18 Dec 12 2021 15:59:24

%S 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,

%T 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,

%U 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

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

%C A179052 and A008592 give record values and where they occur.

%H Reinhard Zumkeller, <a href="/A179051/b179051.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

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

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

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

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

%F 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.

%F G.f.: Product_{k>=0} 1/(1 - x^(10^k)). - _Ilya Gutkovskiy_, Jul 26 2017

%e a(19) = #{10 + 9x1, 19x1} = 2;

%e a(20) = #{10 + 10, 10 + 10x1, 20x1} = 3;

%e a(21) = #{10 + 10 + 1, 10 + 11x1, 21x1} = 3.

%t terms = 10001;

%t CoefficientList[Product[1/(1 - x^(10^k)) + O[x]^terms,

%t      {k, 0, Log[10, terms] // Ceiling}], x]

%t (* _Jean-François Alcover_, Dec 12 2021, after _Ilya Gutkovskiy_ *)

%o (Haskell)

%o a179051 = p 1 where

%o    p _ 0 = 1

%o    p k m = if m < k then 0 else p k (m - k) + p (k * 10) m

%o -- _Reinhard Zumkeller_, Feb 05 2012

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

%Y Cf. A206245, A000041, A179051.

%Y Cf. A133880, A132272.

%Y Cf. A008592, A179052.

%K nonn

%O 0,11

%A _Reinhard Zumkeller_, Jun 27 2010