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A230135 Triangle read by rows: T(n, k) = 1 if ((k mod 4 = 2) and (n mod 2 = 1)) or ((k mod 4 = 0) and (n mod 2 = 0)) else T(n, k) = 0. 2
1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

The T(n, k) triangle is related to the Kn1p sums of the ‘Races with Ties’ triangle A035317. See A230447 for the Kn1p sums and see A180662 for the definitions of these triangle sums.

The row sums lead to three sequences and they can, quite surprisingly, be linked with Alcuin’s sequence A005044, see the formulas.

LINKS

Table of n, a(n) for n=0..104.

E. Mendelson, Races with Ties, Math. Mag. 55 (1982), 170-175.

FORMULA

T(n, k) = 1 if ((k mod 4 = 2) and (n mod 2 = 1)) or ((k mod 4 = 0) and (n mod 2 = 0)) else T(n, k) = 0.

sum(T(n, k), k=0..n) = A008624(n) = A026922(n+2) = A059169(n+3) = A005044(n+3) - A005044(n-3).

EXAMPLE

The first few rows of triangle T(n, k), n >= 0 and 0 <= k <= n.

n/k 0   1   2   3   4   5   6   7

------------------------------------------------

0|  1

1|  0,  0

2|  1,  0,  0

3|  0,  0,  1,  0

4|  1,  0,  0,  0,  1

5|  0,  0,  1,  0,  0,  0

6|  1,  0,  0,  0,  1,  0,  0

7|  0,  0,  1,  0,  0,  0,  1,  0

MAPLE

T := proc(n, k): if ((k mod 4 = 2) and (n mod 2 = 1)) or ((k mod 4 = 0) and (n mod 2 = 0)) then return(1) else return(0) fi: end: seq(seq(T(n, k), k=0..n), n=0..13);

CROSSREFS

Sequence in context: A326072 A304362 A330682 * A205633 A252488 A170956

Adjacent sequences:  A230132 A230133 A230134 * A230136 A230137 A230138

KEYWORD

nonn,easy,tabl

AUTHOR

Johannes W. Meijer, Oct 12 2013

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)