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 A216236 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=5, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1). 4
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 0, 0, 5, 10, 10, 4, 0, 0, 5, 15, 20, 14, 0, 0, 0, 0, 20, 35, 34, 14, 0, 0, 0, 0, 20, 55, 69, 48, 0, 0, 0, 0, 0, 0, 75, 124, 117, 48, 0, 0, 0, 0, 0, 0, 75, 199, 241, 165, 0, 0, 0, 0, 0, 0, 0, 0, 274, 440, 406, 165, 0, 0, 0, 0, 0, 0, 0, 0, 274, 714, 846, 571, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Arithmetic hexagon of E. Lucas. REFERENCES E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome 1, p. 89 LINKS Table of n, a(n) for n=0..90. E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, 1991, p.89 FORMULA T(n+3,n) = T(n+2,n) = A094827(n). T(n+1,n) = A094832(n). T(n,n) = A094854(n). T(n,n+1) = A094855(n). T(n,n+2) = A094833(n+1). T(n,n+3) = T(n,n+4) = A094828(n). Sum( T(n-k,k), 0<=k<=n ) = A217733(n). - Philippe Deléham, Mar 22 2013 EXAMPLE Square array begins: 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ... 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, ... 1, 3, 6, 10, 15, 20, 20, 0, 0, 0, ... 1, 4, 10, 20, 35, 55, 75, 75, 0, 0, 0, ... 0, 4, 14, 34, 69, 124, 199, 274, 274, 0, 0, ... 0, 0, 14, 48, 117, 241, 440, 714, 988, 988, 0, ... ... CROSSREFS Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235. Sequence in context: A349976 A090641 A055216 * A217770 A216219 A180181 Adjacent sequences: A216233 A216234 A216235 * A216237 A216238 A216239 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Mar 14 2013 STATUS approved

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Last modified April 17 10:33 EDT 2024. Contains 371763 sequences. (Running on oeis4.)