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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
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]
Sequence in context: A160089 A259358 A290086 * A308342 A303399 A053597
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 March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)