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