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 A173284 Triangle by columns, Fibonacci numbers in every column shifted down twice, for k>0. 5
 1, 1, 2, 1, 3, 1, 5, 2, 1, 8, 3, 1, 13, 5, 2, 21, 8, 3, 1, 34, 13, 5, 2, 1, 55, 21, 8, 3, 1, 89, 34, 13, 5, 2, 1, 144, 55, 21, 8, 3, 1, 233, 89, 34, 13, 5, 2, 1, 377, 144, 55, 21, 8, 3, 1, 610, 233, 89, 34, 13, 5, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The row sums equal A052952. Let the triangle = M. Then Lim_{n->inf} M^n = A173285 as a left-shifted vector. A173284 * [1, 2, 3,...] = A054451: (1, 1, 4, 5, 12, 17, 33,...) - Gary W. Adamson, Mar 03 2010 From Johannes W. Meijer, Sep 05 2013: (Start) Triangle read by rows formed from antidiagonals of triangle A104762. The diagonal sums lead to A004695. (end) LINKS FORMULA Triangle by columns, Fibonacci numbers in every column shifted down twice, for k>0. From Johannes W. Meijer, Sep 05 2013: (Start) T(n,k) = A000045(n-2*k+1), n >= 0 and 0 <= k <= floor(n/2). T(n,k) = A104762(n-k, k). (End) EXAMPLE First few rows of the triangle = 1; 1; 2, 1; 3, 1; 5, 2, 1; 8, 3, 1; 13, 5, 2, 1; 21, 8, 3, 1; 34, 13, 5, 2, 1; 55, 21, 8, 3, 1; 89, 34, 13, 5, 2, 1; 144, 55, 21, 8, 3, 1; 233, 89, 34, 13, 5, 2, 1; 377, 144, 55, 21, 8, 3, 1; 610, 233, 89, 34, 13, 5, 2, 1; ... MAPLE T := proc(n, k): if n<0 then return(0) elif k < 0 or k > floor(n/2) then return(0) else combinat[fibonacci](n-2*k+1) fi: end: seq(seq(T(n, k), k=0..floor(n/2)), n=0..14); # Johannes W. Meijer, Sep 05 2013 CROSSREFS Cf. A000045, A004695, A052952, A054451, A173285. Cf. (Similar triangles)  A008315 (Catalan), A011973 (Pascal), A102541 (Losanitsch), A122196 (Fractal), A122197 (Fractal), A128099 (Pell-Jacobsthal), A152198, A152204, A207538, A209634. Sequence in context: A147486 A168018 A173238 * A278136 A085053 A296118 Adjacent sequences:  A173281 A173282 A173283 * A173285 A173286 A173287 KEYWORD nonn,tabf AUTHOR Gary W. Adamson, Feb 14 2010 EXTENSIONS Term a(15) corrected by Johannes W. Meijer, Sep 05 2013 STATUS approved

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Last modified August 4 00:29 EDT 2021. Contains 346441 sequences. (Running on oeis4.)