OFFSET
0,3
COMMENTS
This sequence is related to the Connell sequence (A001614).
First member of every row is a square (A000290).
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
Written as a square array the main diagonal gives A002943. - Omar E. Pol, Aug 13 2013
Last member of every row is one less than a square (A005563). - Harvey P. Dale, Oct 02 2013
LINKS
Reinhard Zumkeller, Rows n=0..100 of triangle, flattened
FORMULA
T(n,k) = n^2 + 2*k. - Joerg Arndt, Aug 13 2013
EXAMPLE
Written as a triangle the sequence begins:
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, 44, 46, 48;
49, 51, 53, 55, 57, 59, 61, 63;
64, 66, 68, 70, 72, 74, 76, 78, 80;
81, 83, 85, 87, 89, 91, 93, 95, 97, 99;
100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120;
MATHEMATICA
Flatten[Table[Range[(n-1)^2, n^2-1, 2], {n, 20}]] (* Harvey P. Dale, Oct 02 2013 *)
PROG
(Haskell)
a133280 n k = a133280_tabl !! n !! k
a133280_tabl = f 0 1 [0..] where
f m j xs = (filter ((== m) . (`mod` 2)) ys) : f (1 - m) (j + 2) xs'
where (ys, xs') = splitAt j xs
b133280 = bFile' "A133280" (concat $ take 101 a133280_tabl) 0
-- Reinhard Zumkeller, Oct 12 2011
(PARI) T(n, k) = n^2 + 2*k;
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))); \\ Joerg Arndt, Aug 13 2013
(Python)
from math import isqrt
def A133280(n): return (m:=(n<<1)+1)-((isqrt(m+1<<2)+1)>>1) # Chai Wah Wu, Aug 01 2022
CROSSREFS
KEYWORD
AUTHOR
Omar E. Pol, Aug 27 2008
STATUS
approved