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 A129363 #20 Sep 16 2024 15:31:27
%S A129363 0,0,1,1,2,1,2,2,2,2,3,3,2,1,2,2,3,3,2,1,2,2,3,4,2,1,2,1,2,3,3,2,2,1,
%T A129363 2,4,3,3,4,2,2,3,2,2,4,2,0,0,0,2,4,3,2,2,2,4,6,3,3,5,3,1,2,1,2,4,2,1,
%U A129363 2,2,4,5,3,2,4,3,3,4,2,2,4,2,3,6,3,1,2,1,3,6,4,2,2,1,2,4,3,4,6,4,4,5,3,6,12
%N A129363 Number of partitions of 2n into the sum of two twin primes.
%C A129363 a(n/2)=0 for the n in A007534. The logarithmic plot of this sequence seems very regular after 200000 terms.
%H A129363 T. D. Noe, <a href="/A129363/b129363.txt">Table of n, a(n) for n=1..10000</a>
%H A129363 James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=Gojd8mTl3Do">Goldbach Conjecture (but with TWIN PRIMES)</a>, Numberphile video (2024)
%H A129363 T. D. Noe, <a href="http://www.sspectra.com/math/A129363.gif">Logarithmic plot of 10^6 terms</a>
%F A129363 a(n) = Sum_{i=1..n} ceiling((A010051(i+2) + A010051(i-2))/2) * ceiling((A010051(2n-i+2) + A010051(2n-i-2))/2) * A010051(2n-i) * A010051(i). - _Wesley Ivan Hurt_, Jan 30 2014
%F A129363 a(n) = sum(A164292(2*n - A001097(k)): A001097(k) <= n). - _Reinhard Zumkeller_, Feb 03 2014
%e A129363 a(11)=3 because 22 = 3+19 = 5+17 = 11+11.
%t A129363 nn=1000; tw=Select[Prime[Range[PrimePi[nn]]], PrimeQ[ #+2]&]; tw=Union[tw,tw+2]; tc=Table[0,{nn}]; tc[[tw]]=1; Table[cnt=0; k=1; While[tw[[k]]<=n/2, cnt=cnt+tc[[n-tw[[k]]]]; k++ ]; cnt, {n,2,nn,2}]
%o A129363 (Haskell)
%o A129363 a129363 n = sum $ map (a164292 . (2*n -)) $ takeWhile (<= n) a001097_list
%o A129363 -- _Reinhard Zumkeller_, Feb 03 2014
%Y A129363 Cf. A175931 (n for which a(n-1), a(n), a(n+1) are equal).
%Y A129363 Cf. A001097, A002375, A007534.
%K A129363 nonn
%O A129363 1,5
%A A129363 _T. D. Noe_, Apr 11 2007
%E A129363 Comment converted to crossref by _Klaus Brockhaus_, Oct 27 2010