cp's OEIS Frontend

A354600 a(n) = Product_{k=0..9} floor((n+k)/10).

%I A354600 #27 Mar 19 2025 08:23:48
%S A354600 0,0,0,0,0,0,0,0,0,0,1,2,4,8,16,32,64,128,256,512,1024,1536,2304,3456,
%T A354600 5184,7776,11664,17496,26244,39366,59049,78732,104976,139968,186624,
%U A354600 248832,331776,442368,589824,786432,1048576,1310720,1638400,2048000,2560000,3200000,4000000
%N A354600 a(n) = Product_{k=0..9} floor((n+k)/10).
%C A354600 For n >= 10, a(n) is the maximal product of ten positive integers with sum n.
%H A354600 <a href="/index/Rec#order_92">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 9, -18, 9, 0, 0, 0, 0, 0, 0, 0, -36, 72, -36, 0, 0, 0, 0, 0, 0, 0, 84, -168, 84, 0, 0, 0, 0, 0, 0, 0, -126, 252, -126, 0, 0, 0, 0, 0, 0, 0, 126, -252, 126, 0, 0, 0, 0, 0, 0, 0, -84, 168, -84, 0, 0, 0, 0, 0, 0, 0, 36, -72, 36, 0, 0, 0, 0, 0, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).
%H A354600 <a href="/index/Su#sublatts">Index entries for subsets of {1,..,n} with disallowed differences</a>
%F A354600 a(n) = 2*a(n-1) - a(n-2) + 9*a(n-10) - 18*a(n-11) + 9*a(n-12) - 36*a(n-20) + 72*a(n-21) - 36*a(n-22) + 84*a(n-30) - 168*a(n-31) + 84*a(n-32) - 126*a(n-40) + 252*a(n-41) - 126*a(n-42) + 126*a(n-50) - 252*a(n-51) + 126*a(n-52) - 84*a(n-60) + 168*a(n-61) - 84*a(n-62) + 36*a(n-70) - 72*a(n-71) + 36*a(n-72) - 9*a(n-80) + 18*a(n-81) - 9*a(n-82) + a(n-90) - 2*a(n-91) + a(n-92).
%F A354600 Sum_{n>=10} 1/a(n) = 1 + zeta(10). - _Amiram Eldar_, Jan 10 2023
%F A354600 a(10*n) = n^10 (A008454). - _Bernard Schott_, Feb 02 2023
%t A354600 Table[Product[Floor[(n + k)/10], {k, 0, 9}], {n, 0, 50}]
%o A354600 (PARI) a(n) = prod(k=0, 9, (n+k)\10); \\ _Michel Marcus_, Jul 09 2022
%Y A354600 Maximal product of k positive integers with sum n, for k = 2..10: A002620 (k=2), A006501 (k=3), A008233 (k=4), A008382 (k=5), A008881 (k=6), A009641 (k=7), A009694 (k=8), A009714 (k=9), this sequence (k=10).
%Y A354600 Cf. A008454 (subsequence), A013668.
%K A354600 nonn,easy
%O A354600 0,12
%A A354600 _Wesley Ivan Hurt_, Jul 08 2022