cp's OEIS Frontend

A007607 Skip 1, take 2, skip 3, etc.

%I A007607 M0821 #72 Feb 10 2023 12:54:13
%S A007607 2,3,7,8,9,10,16,17,18,19,20,21,29,30,31,32,33,34,35,36,46,47,48,49,
%T A007607 50,51,52,53,54,55,67,68,69,70,71,72,73,74,75,76,77,78,92,93,94,95,96,
%U A007607 97,98,99,100,101,102,103,104,105,121,122,123,124,125,126,127,128,129,130
%N A007607 Skip 1, take 2, skip 3, etc.
%C A007607 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
%C A007607 Union of A317303 and A014105. - _Omar E. Pol_, Aug 29 2018
%D A007607 R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.
%D A007607 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007607 Reinhard Zumkeller, <a href="/A007607/b007607.txt">Table of n, a(n) for n = 1..10000</a>
%F A007607 G.f.: 1/(1-x) * (1/(1-x) + x*Sum_{k>=1} (2k+1)*x^(k*(k+1))). - _Ralf Stephan_, Mar 03 2004
%F A007607 a(A000290(n)) = A001105(n). - _Reinhard Zumkeller_, Feb 12 2011
%F A007607 A057211(a(n)) = 0. - _Reinhard Zumkeller_, Dec 30 2011
%F A007607 a(n) = floor(sqrt(n) + 1/2)^2 + n = A053187(n) + n. - _Ridouane Oudra_, May 04 2019
%e A007607 From _Omar E. Pol_, Aug 29 2018: (Start)
%e A007607 Written as an irregular triangle in which the row lengths are the nonzero even numbers the sequence begins:
%e A007607     2,   3;
%e A007607     7,   8,   9,  10;
%e A007607    16,  17,  18,  19,  20,  21;
%e A007607    29,  30,  31,  32,  33,  34,  35,  36;
%e A007607    46,  47,  48,  49,  50,  51,  52,  53,  54,  55;
%e A007607    67,  68,  69,  70,  71,  72,  73,  74,  75,  76,  77,  78;
%e A007607    92,  93,  94,  95,  96,  97,  98,  99, 100, 101, 102, 103, 104, 105;
%e A007607   121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136;
%e A007607 ...
%e A007607 Row sums give the nonzero terms of A317297.
%e A007607 Column 1 gives A130883, n >= 1.
%e A007607 Right border gives A014105, n >= 1.
%e A007607 (End)
%t A007607 Flatten[ Table[i, {j, 2, 16, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (* _Robert G. Wilson v_, Mar 11 2004 *)
%t A007607 With[{t=20},Flatten[Take[TakeList[Range[(t(t+1))/2],Range[t]],{2,-1,2}]]] (* _Harvey P. Dale_, Sep 26 2021 *)
%o A007607 (Haskell)
%o A007607 a007607 n = a007607_list !! (n-1)
%o A007607 a007607_list = skipTake 1 [1..] where
%o A007607    skipTake k xs = take (k + 1) (drop k xs)
%o A007607                    ++ skipTake (k + 2) (drop (2*k + 1) xs)
%o A007607 -- _Reinhard Zumkeller_, Feb 12 2011
%o A007607 (PARI) for(m=0,10,for(n=2*m^2+3*m+2,2*m^2+5*m+3,print1(n", "))) \\ _Charles R Greathouse IV_, Feb 12 2011
%o A007607 (Haskell)
%o A007607 a007607_list' = f $ tail $ scanl (+) 0 [1..] where
%o A007607    f (t:t':t'':ts) = [t+1..t'] ++ f (t'':ts)
%o A007607 -- _Reinhard Zumkeller_, Feb 12 2011
%Y A007607 Cf. A063656, A004202, A063657, A007606, A064801, A004202.
%Y A007607 Complement of A007606.
%Y A007607 Cf. A014105, A130883, A317297.
%Y A007607 Similar to A360418.
%K A007607 nonn,easy,tabf
%O A007607 1,1
%A A007607 _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_