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 A129363 Number of partitions of 2n into the sum of two twin primes. 15
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(n/2)=0 for the n in A007534. The logarithmic plot of this sequence seems very regular after 200000 terms LINKS T. D. Noe, Table of n, a(n) for n=1..10000 T. D. Noe, Logarithmic plot of 10^6 terms FORMULA 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 a(n) = sum(A164292(2*n - A001097(k)): A001097(k) <= n). - Reinhard Zumkeller, Feb 03 2014 EXAMPLE a(11)=3 because 22 = 3+19 = 5+17 = 11+11. MATHEMATICA 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}] PROG (Haskell) a129363 n = sum \$ map (a164292 . (2*n -)) \$ takeWhile (<= n) a001097_list -- Reinhard Zumkeller, Feb 03 2014 CROSSREFS Cf. A175931 (n for which a(n-1), a(n), a(n+1) are equal). [From Juri-Stepan Gerasimov, Oct 23 2010] Cf. A001097, A002375. Sequence in context: A160089 A259358 A290086 * A308342 A303399 A053597 Adjacent sequences: A129360 A129361 A129362 * A129364 A129365 A129366 KEYWORD nonn AUTHOR T. D. Noe, Apr 11 2007 EXTENSIONS Comment converted to crossref by Klaus Brockhaus, Oct 27 2010 STATUS approved

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Last modified June 3 14:22 EDT 2023. Contains 363116 sequences. (Running on oeis4.)