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 A217257 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 7, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,3) = T(0,4) = T(0,5) = T(0,6) = 1, T(n,k) = T(n-1,k) + T(n,k-1). 3
 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 1, 5, 9, 5, 0, 0, 0, 0, 6, 14, 14, 0, 0, 0, 0, 0, 6, 20, 28, 14, 0, 0, 0, 0, 0, 0, 26, 48, 42, 0, 0, 0, 0, 0, 0, 0, 26, 74, 90, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 164, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 264, 296, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364, 560, 428, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS A hexagon arithmetic of E. Lucas. REFERENCES E. Lucas, Théorie des nombres, A. Blanchard, Paris, 1958, p.89 LINKS E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, p. 89 FORMULA T(n,n) = A024175(n). T(n,n+1) = A024175(n+1). T(n,n+2) = A094803(n+1). T(n,n+3) = A007070(n). T(n,n+4) = A094806(n+2). T(n,n+5) = T(n,n+6) = A094811(n+2). Sum_{k, 0<=k<=n} T(n-k,k) = A030436(n). EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0 0, 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1 0, 0, 2, 5, 9, 14, 20, 26, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=2 0, 0, 0, 5, 14, 28, 48, 74, 100, 100, 0, 0, 0, 0, 0, 0, 0, ... row n=3 0, 0, 0, 0, 14, 42, 90, 162, 264, 364, 364, 0, 0, 0, 0, 0, ... row n=4 0, 0, 0, 0, 0, 42, 132, 296, 560, 924, 1288, 1288, 0, 0, 0, ... row n=5 ... CROSSREFS Cf. similar sequences: A216230, A216228, A216226, A216238, A216054. Sequence in context: A157608 A220062 A216054 * A217315 A217593 A322279 Adjacent sequences:  A217254 A217255 A217256 * A217258 A217259 A217260 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Mar 17 2013 STATUS approved

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Last modified November 23 16:18 EST 2020. Contains 338590 sequences. (Running on oeis4.)