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A007607
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Skip 1, take 2, skip 3, etc.
(Formerly M0821)
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10
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2, 3, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 29, 30, 31, 32, 33, 34, 35, 36, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130
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OFFSET
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1,1
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COMMENTS
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Numbers k with the property that the smallest Dyck path of the symmetric representation of sigma(k) has a central peak. (Cf. A237593.) - Omar E. Pol, Aug 28 2018
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REFERENCES
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R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: 1/(1-x) * (1/(1-x) + x*Sum_{k>=1} (2k+1)*x^(k*(k+1))). - Ralf Stephan, Mar 03 2004
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EXAMPLE
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Written as an irregular triangle in which the row lengths are the nonzero even numbers the sequence begins:
2, 3;
7, 8, 9, 10;
16, 17, 18, 19, 20, 21;
29, 30, 31, 32, 33, 34, 35, 36;
46, 47, 48, 49, 50, 51, 52, 53, 54, 55;
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78;
92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105;
121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136;
...
Row sums give the nonzero terms of A317297.
Right border gives A014105, n >= 1.
(End)
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MATHEMATICA
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Flatten[ Table[i, {j, 2, 16, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (* Robert G. Wilson v, Mar 11 2004 *)
With[{t=20}, Flatten[Take[TakeList[Range[(t(t+1))/2], Range[t]], {2, -1, 2}]]] (* Harvey P. Dale, Sep 26 2021 *)
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PROG
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(Haskell)
a007607 n = a007607_list !! (n-1)
a007607_list = skipTake 1 [1..] where
skipTake k xs = take (k + 1) (drop k xs)
++ skipTake (k + 2) (drop (2*k + 1) xs)
(Haskell)
a007607_list' = f $ tail $ scanl (+) 0 [1..] where
f (t:t':t'':ts) = [t+1..t'] ++ f (t'':ts)
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CROSSREFS
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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