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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.)