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A129363 Number of partitions of 2n into the sum of two twin primes. 11
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: A086376 A160089 A259358 * A053597 A230197 A094570

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 May 27 07:51 EDT 2017. Contains 287202 sequences.