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A133280 Triangle formed by: 1 even, 2 odd, 3 even, 4 odd... starting with zero. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Column 1 is A000290. Right border gives A005563.

Cf. A001614.

Cf. A045991 (row sums). [From 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

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Last modified February 21 10:51 EST 2018. Contains 299390 sequences. (Running on oeis4.)