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

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

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

a(n) = A005408(n) - A002024(n+1). - Ivan N. Ianakiev, Aug 13 2013

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

Column 1 is A000290. Right border gives A005563.

Cf. A001614.

Cf. A045991 (row sums). - R. J. Mathar, Jul 20 2009

Sequence in context: A187474 A081031 A285681 * A280762 A138097 A193732

Adjacent sequences: A133277 A133278 A133279 * A133281 A133282 A133283

Keyword

easy,nonn,tabl

Author

Omar E. Pol, Aug 27 2008

Status

approved