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A133280 Triangle formed by: 1 even, 2 odd, 3 even, 4 odd, ... starting with zero.

%I A133280 #50 Aug 01 2022 14:23:10
%S A133280 0,1,3,4,6,8,9,11,13,15,16,18,20,22,24,25,27,29,31,33,35,36,38,40,42,
%T A133280 44,46,48,49,51,53,55,57,59,61,63,64,66,68,70,72,74,76,78,80,81,83,85,
%U A133280 87,89,91,93,95,97,99,100,102,104,106,108,110,112,114,116,118,120
%N A133280 Triangle formed by: 1 even, 2 odd, 3 even, 4 odd, ... starting with zero.
%C A133280 This sequence is related to the Connell sequence (A001614).
%C A133280 First member of every row is a square (A000290).
%C A133280 A127366(T(n,k)) mod 2 = 0 or equal parity of T(n,k) and A000196(T(n,k)); complement of A195437. - _Reinhard Zumkeller_, Oct 12 2011
%C A133280 Written as a square array the main diagonal gives A002943. - _Omar E. Pol_, Aug 13 2013
%C A133280 Last member of every row is one less than a square (A005563). - _Harvey P. Dale_, Oct 02 2013
%H A133280 Reinhard Zumkeller, <a href="/A133280/b133280.txt">Rows n=0..100 of triangle, flattened</a>
%F A133280 a(n) = A005408(n) - A002024(n+1). - _Ivan N. Ianakiev_, Aug 13 2013
%F A133280 T(n,k) = n^2 + 2*k. - _Joerg Arndt_, Aug 13 2013
%e A133280 Written as a triangle the sequence begins:
%e A133280     0;
%e A133280     1,   3;
%e A133280     4,   6,   8;
%e A133280     9,  11,  13,  15;
%e A133280    16,  18,  20,  22,  24;
%e A133280    25,  27,  29,  31,  33,  35;
%e A133280    36,  38,  40,  42,  44,  46,  48;
%e A133280    49,  51,  53,  55,  57,  59,  61,  63;
%e A133280    64,  66,  68,  70,  72,  74,  76,  78,  80;
%e A133280    81,  83,  85,  87,  89,  91,  93,  95,  97,  99;
%e A133280   100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120;
%t A133280 Flatten[Table[Range[(n-1)^2,n^2-1,2],{n,20}]] (* _Harvey P. Dale_, Oct 02 2013 *)
%o A133280 (Haskell)
%o A133280 a133280 n k = a133280_tabl !! n !! k
%o A133280 a133280_tabl = f 0 1 [0..] where
%o A133280    f m j xs = (filter ((== m) . (`mod` 2)) ys) : f (1 - m) (j + 2) xs'
%o A133280      where (ys,xs') = splitAt j xs
%o A133280 b133280 = bFile' "A133280" (concat $ take 101 a133280_tabl) 0
%o A133280 -- _Reinhard Zumkeller_, Oct 12 2011
%o A133280 (PARI) T(n,k) = n^2 + 2*k;
%o A133280 for(n=0,10,for(k=0,n,print1(T(n,k),", "))); \\ _Joerg Arndt_, Aug 13 2013
%o A133280 (Python)
%o A133280 from math import isqrt
%o A133280 def A133280(n): return (m:=(n<<1)+1)-((isqrt(m+1<<2)+1)>>1) # _Chai Wah Wu_, Aug 01 2022
%Y A133280 Column 1 is A000290. Right border gives A005563.
%Y A133280 Cf. A001614.
%Y A133280 Cf. A045991 (row sums). - _R. J. Mathar_, Jul 20 2009
%K A133280 easy,nonn,tabl
%O A133280 0,3
%A A133280 _Omar E. Pol_, Aug 27 2008