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A215189 Array t(n,k) of the family ((n+k)/gcd(n+k,4))*(n/gcd(n,4)), read by antidiagonals. 1
0, 1, 0, 1, 1, 0, 9, 3, 3, 0, 1, 3, 1, 1, 0, 25, 5, 15, 5, 5, 0, 9, 15, 3, 9, 3, 3, 0, 49, 21, 35, 7, 21, 7, 7, 0, 4, 14, 6, 10, 2, 6, 2, 2, 0, 81, 18, 63, 27, 45, 9, 27, 9, 9, 0, 25, 45, 10, 35, 15, 25, 5, 15, 5, 5, 0, 121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11, 0, 9, 33, 15, 27, 6, 21, 9, 15, 3, 9, 3, 3, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Identification of rows and columns:

Row 2, n=1: A060819,

row 3, n=2: A060819 (shifted),

row 4, n=3: A068219,

row 5, n=4: A060819 (shifted),

row 6, n=5: A060819 (shifted and multiplied by 5),

row 7, n=6: A068219 (shifted),

row 8, n=7: A060819 (shifted and multiplied by 7);

column 1, k=0: A181318,

column 2, k=1: A064038,

column 3, k=2: A198148,

column 4, k=3: A160050,

column 5, k=4: A061037,

column 6, k=5: A178242,

column 7, k=6: A217366,

column 8, k=7: A217367.

This array is the transposition of the array given by Paul Curtz in the comments in A181318.

LINKS

G. C. Greubel, Antidiagonals n=0..100 of triangle, flattened

FORMULA

t(n,k) = ((n+k)/gcd(n+k,4))*(n/gcd(n,4)).

EXAMPLE

Array begins:

   0,  0,  0,  0,  0,  0,  0, ...

   1,  1,  3,  1,  5,  3,  7, ...

   1,  3,  1,  5,  3,  7,  2, ...

   9,  3, 15,  9, 21,  6, 27, ...

   1,  5,  3,  7,  2,  9,  5, ...

  25, 15, 35, 10, 45, 25, 55, ...

   9, 21,  6, 27, 15, 33,  9, ...

  49, 14, 63, 35, 77, 21, 91, ...

  ...

Triangle begins:

    0;

    1,  0;

    1,  1,  0;

    9,  3,  3,  0;

    1,  3,  1,  1,  0;

   25,  5, 15,  5,  5,  0;

    9, 15,  3,  9,  3,  3,  0;

   49, 21, 35,  7, 21,  7,  7,  0;

    4, 14,  6, 10,  2,  6,  2,  2,  0;

   81, 18, 63, 27, 45,  9, 27,  9,  9,  0;

   25, 45, 10, 35, 15, 25,  5, 15,  5,  5,  0;

  121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11,  0;

    9, 33, 15, 27,  6, 21,  9, 15,  3,  9,  3,  3,  0;

  ...

MATHEMATICA

t[n_, k_] := (n+k)/GCD[n+k, 4]*n/GCD[n, 4];  Table[t[n-k, k], {n, 0, 12}, {k, 0, n}] // Flatten

PROG

(MAGMA) /* As triangle: */ [[(n-k)/GCD(n-k, 4)*n/GCD(n, 4): k in [0..n]]: n in [0..12]]; // Bruno Berselli, Jun 13 2013

CROSSREFS

Cf. A060819, A181318, A064038, A198148, A160050, A061037, A178242, A217366, A217367.

Sequence in context: A019721 A265162 A259837 * A201320 A212436 A193015

Adjacent sequences:  A215186 A215187 A215188 * A215190 A215191 A215192

KEYWORD

nonn,tabl

AUTHOR

Jean-Fran├žois Alcover, Jun 12 2013

STATUS

approved

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Last modified October 19 11:57 EDT 2018. Contains 316359 sequences. (Running on oeis4.)