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A067953
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Number of ways to sum numbers from 1 to n to the n-th prime.
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6
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0, 1, 1, 2, 2, 4, 7, 13, 23, 39, 69, 122, 211, 339, 564, 1001, 1764, 2630, 4565, 7192, 10151, 17202, 26152, 43543, 79126, 117496, 156229, 227302, 295011, 422040, 1004905, 1423445, 2210752, 2796140, 5225780, 6546101, 9921635, 14947534
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| a(n) = b(0, n), where b(m, n) satisfies b(m, n) = 1 + sum{b(i, j): m<i<j<n & i+j=prime(n)}.
a(n) < A000009(A000040(n)).
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EXAMPLE
| a(6)=4, as there are 4 decompositions for A000040(6)=13:
6+5+2 = 6+4+3 = 6+4+2+1 = 5+4+3+1 = 13.
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PROG
| (Haskell)
a067953 n = p [1..n] $ a000040 n where
p _ 0 = 1
p [] _ = 0
p (k:ks) m | m < k = 0 | otherwise = p ks (m - k) + p ks m
-- Reinhard Zumkeller, Nov 22 2011
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CROSSREFS
| Sequence in context: A179183 A095325 A153970 * A109070 A169973 A049868
Adjacent sequences: A067950 A067951 A067952 * A067954 A067955 A067956
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KEYWORD
| nonn,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 06 2002
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EXTENSIONS
| a(36)-a(38) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 23 2010
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