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A098172 Triangle T(n,k) with diagonals T(n,n-k) = binomial(n,3k). 3
1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 1, 20, 1, 0, 0, 0, 0, 0, 7, 35, 1, 0, 0, 0, 0, 0, 0, 28, 56, 1, 0, 0, 0, 0, 0, 0, 1, 84, 84, 1, 0, 0, 0, 0, 0, 0, 0, 10, 210, 120, 1, 0, 0, 0, 0, 0, 0, 0, 0, 55, 462, 165, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 220, 924, 220, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

Row sums are A024493.

From R. J. Mathar, Mar 22 2013: (Start)

The matrix inverse starts

  1;

  0, 1;

  0, 0,      1;

  0, 0,     -1,     1;

  0, 0,      4,    -4,     1;

  0, 0,    -40,    40,   -10,   1;

  0, 0,    796,  -796,   199, -20,   1;

  0, 0, -27580, 27580, -6895, 693, -35, 1;

  ... (End)

LINKS

Seiichi Manyama, Rows n = 0..139, flattened

FORMULA

Triangle T(n, k) = binomial(n, 3(n-k)).

EXAMPLE

Rows begin

  {1},

  {0,1},

  {0,0,1},

  {0,0,1,1},

  {0,0,0,4,1},

  {0,0,0,0,10,1},

  ...

MATHEMATICA

Table[Binomial[n, 3(n-k)], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 15 2019 *)

PROG

(PARI) {T(n, k) = binomial(n, 3*(n-k))}; \\ G. C. Greubel, Mar 15 2019

(MAGMA) [[Binomial(n, 3*(n-k)): k in [0..n]]: n in [0..12]]; // G. C. Greubel, Mar 15 2019

(Sage) [[binomial(n, 3*(n-k)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 15 2019

(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, 3*(n-k)) ))); # G. C. Greubel, Mar 15 2019

CROSSREFS

Cf. A098158.

Sequence in context: A093318 A255329 A127560 * A049759 A265421 A137252

Adjacent sequences:  A098169 A098170 A098171 * A098173 A098174 A098175

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Aug 30 2004

STATUS

approved

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Last modified July 27 04:54 EDT 2021. Contains 346305 sequences. (Running on oeis4.)