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%I A111837 #15 Jun 13 2017 22:36:36
%S A111837 1,2,10,298,53674,58573738,409251498922,19046062579215274,
%T A111837 6071277235712979102634,13531779463193107731083553706,
%U A111837 214224474679766323250278564215516074,24390479071277895100812271376578637910371242,20173309182842708837666031701435147789403500172143530
%N A111837 Number of partitions of 8^n into powers of 8, also equals the row sums of triangle A111835, which shifts columns left and up under matrix 8th power.
%H A111837 Alois P. Heinz, <a href="/A111837/b111837.txt">Table of n, a(n) for n = 0..45</a>
%F A111837 a(n) = [x^(8^n)] 1/Product_{j>=0} (1-x^(8^j)).
%o A111837 (PARI) a(n,q=8)=local(A=Mat(1),B);if(n<0,0, for(m=1,n+2,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i || j==1,B[i,j]=1,B[i,j]=(A^q)[i-1,j-1]);));A=B); return(sum(k=0,n,A[n+1,k+1])))
%Y A111837 Cf. A111835, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111827 (q=6), A111832 (q=7). Column 8 of A145515.
%K A111837 nonn
%O A111837 0,2
%A A111837 _Gottfried Helms_ and _Paul D. Hanna_, Aug 22 2005

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