cp's OEIS Frontend

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

%I A179051 #18 Dec 12 2021 15:59:24
%S A179051 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 A179051 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 A179051 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 A179051 Number of partitions of n into powers of 10 (cf. A011557).
%C A179051 A179052 and A008592 give record values and where they occur.
%H A179051 Reinhard Zumkeller, <a href="/A179051/b179051.txt">Table of n, a(n) for n = 0..10000</a>
%H A179051 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A179051 a(n) = A133880(n) for n < 90; a(n) = A132272(n) for n < 100.
%F A179051 a(10^n) = A145513(n).
%F A179051 a(10*n) = A179052(n).
%F A179051 A179052(n) = a(A008592(n));
%F A179051 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 A179051 G.f.: Product_{k>=0} 1/(1 - x^(10^k)). - _Ilya Gutkovskiy_, Jul 26 2017
%e A179051 a(19) = #{10 + 9x1, 19x1} = 2;
%e A179051 a(20) = #{10 + 10, 10 + 10x1, 20x1} = 3;
%e A179051 a(21) = #{10 + 10 + 1, 10 + 11x1, 21x1} = 3.
%t A179051 terms = 10001;
%t A179051 CoefficientList[Product[1/(1 - x^(10^k)) + O[x]^terms,
%t A179051      {k, 0, Log[10, terms] // Ceiling}], x]
%t A179051 (* _Jean-François Alcover_, Dec 12 2021, after _Ilya Gutkovskiy_ *)
%o A179051 (Haskell)
%o A179051 a179051 = p 1 where
%o A179051    p _ 0 = 1
%o A179051    p k m = if m < k then 0 else p k (m - k) + p (k * 10) m
%o A179051 -- _Reinhard Zumkeller_, Feb 05 2012
%Y A179051 Number of partitions of n into powers of b: A018819 (b=2), A062051 (b=3).
%Y A179051 Cf. A206245, A000041, A179051.
%Y A179051 Cf. A133880, A132272.
%Y A179051 Cf. A008592, A179052.
%K A179051 nonn
%O A179051 0,11
%A A179051 _Reinhard Zumkeller_, Jun 27 2010