This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009641 #45 Jan 17 2025 07:33:03
%S A009641 0,0,0,0,0,0,0,1,2,4,8,16,32,64,128,192,288,432,648,972,1458,2187,
%T A009641 2916,3888,5184,6912,9216,12288,16384,20480,25600,32000,40000,50000,
%U A009641 62500,78125,93750,112500,135000,162000,194400,233280,279936,326592,381024
%N A009641 a(n) = Product_{i=0..6} floor((n+i)/7).
%C A009641 For n >= 7, a(n) is the maximal product of seven positive integers with sum n. - _Wesley Ivan Hurt_, Jun 29 2022
%H A009641 Paolo Xausa, <a href="/A009641/b009641.txt">Table of n, a(n) for n = 0..10000</a>
%H A009641 M. El-Mikkawy and T. Sogabe, <a href="https://doi.org/10.1016/j.amc.2009.12.069">A new family of k-Fibonacci numbers</a>, Appl. Math. Comput. 215 (2010) 4456-4461, Table 1 k=7.
%H A009641 <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 6, -12, 6, 0, 0, 0, 0, -15, 30, -15, 0, 0, 0, 0, 20, -40, 20, 0, 0, 0, 0, -15, 30, -15, 0, 0, 0, 0, 6, -12, 6, 0, 0, 0, 0, -1, 2, -1).
%F A009641 a(n) = 2*a(n-1) - a(n-2) + 6*a(n-7) - 12*a(n-8) + 6*a(n-9) - 15*a(n-14) + 30*a(n-15) - 15*a(n-16) + 20*a(n-21) - 40*a(n-22) + 20*a(n-23) - 15*a(n-28) + 30*a(n-29) - 15*a(n-30) + 6*a(n-35) - 12*a(n-36) + 6*a(n-37) - a(n-42) + 2*a(n-43) - a(n-44). - _Wesley Ivan Hurt_, Jun 29 2022
%F A009641 a(7*n) = n^7 (A001015). - _Bernard Schott_, Nov 04 2022
%F A009641 Sum_{n>=7} 1/a(n) = 1 + zeta(7). - _Amiram Eldar_, Jan 10 2023
%t A009641 A009641[n_] := Product[Floor[(n + i)/7], {i, 0, 6}]; Array[A009641, 50, 0] (* _Paolo Xausa_, Jan 17 2025 *)
%o A009641 (PARI) a(n) = prod(k=0, 6, (n+k)\7); \\ _Georg Fischer_, Nov 07 2019
%Y A009641 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), this sequence (k=7), A009694 (k=8), A009714 (k=9), A354600 (k=10).
%Y A009641 Cf. A001015, A013665.
%K A009641 nonn,easy
%O A009641 0,9
%A A009641 _N. J. A. Sloane_
%E A009641 a(40)-a(44) from _Georg Fischer_, Nov 07 2019