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 A376024 #16 Sep 20 2024 06:23:58 %S A376024 1,1,1,1,1,3,3,11,35,83,545,2513,13905,152721,1087873,14651923, %T A376024 238834051,3135275371,91466933731,2155382231811,63058059937761, %U A376024 3261572372004353,120654520736448833,8395343248160222081,661217270644238022305,46110296193095128622723,6786635441262507324649635 %N A376024 a(0..4) = 1 and a(n) = (a(n-2)^2 + a(n-3)^2 + a(n-2)*(3*a(n-3) + a(n-4)) + a(n-1)*(a(n-3) - a(n-5)))/(a(n-4) + a(n-5)) for n > 4. %C A376024 An example of how a Somos recurrence can be generalized such that proving its integrality looks more difficult in the first glance. In this example the Somos-4 recurrence b(n) = (b(n-1) * b(n-3) + b(n-2)^2) / b(n-4) was modified by substitution of b(n-k) with (a(n-k) + a(n-k-1)). %C A376024 This sequence is not a divisibility sequence unlike Somos-4 sequences are. %F A376024 (a(n) + a(n+1))/2 = A006720(n). %o A376024 (PARI) a=vector(26); a[1]=a[2]=a[3]=a[4]=a[5]=1; for(n=6, #a, a[n]=(a[n-2]^2+a[n-3]^2+a[n-2]*(3*a[n-3]+a[n-4])+a[n-1]*(a[n-3]-a[n-5]))/(a[n-4]+a[n-5])); a %Y A376024 Cf. A006720, A097495 ( first 6 values coincidence with odd terms ). %K A376024 nonn %O A376024 0,6 %A A376024 _Thomas Scheuerle_, Sep 06 2024