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 A109754 Matrix defined by: a(i,0) = 0, a(i,j) = i*Fibonacci(j-1) + Fibonacci(j), for j > 0; read by antidiagonals. 28
 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 3, 3, 0, 1, 4, 4, 5, 5, 0, 1, 5, 5, 7, 8, 8, 0, 1, 6, 6, 9, 11, 13, 13, 0, 1, 7, 7, 11, 14, 18, 21, 21, 0, 1, 8, 8, 13, 17, 23, 29, 34, 34, 0, 1, 9, 9, 15, 20, 28, 37, 47, 55, 55, 0, 1, 10, 10, 17, 23, 33, 45, 60, 76, 89, 89 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Lower triangular version is at A117501. - Ross La Haye, Apr 12 2006 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA a(i, 0) = 0, a(i, j) = i*Fibonacci(j-1) + Fibonacci(j), for j > 0. a(i, 0) = 0, a(i, 1) = 1, a(i, 2) = i+1, a(i, j) = a(i, j-1) + a(i, j-2), for j > 2. G.f.: (x(1+ix))/(1-x-x^2). Sum_{j=0..i+1} a(i-j+1, j) - Sum_{j=0..i} a(i-j, j) = A001595(i). - Ross La Haye, Jun 03 2006 EXAMPLE {0}; {0,1}; {0,1,1}; {0,1,2,2}; {0,1,3,3,3}; {0,1,4,4,5,5}; {0,1,5,5,7,8,8} MATHEMATICA T[n_, 0]:= 0; T[n_, 1]:= 1; T[n_, 2]:= n - 1; T[n_, 3]:= n - 1; T[n_, n_]:= Fibonacci[n]; T[n_, k_]:= T[n, k] = T[n - 1, k - 1] + T[n - 2, k - 2]; Table[T[n, k], {n, 0, 15}, {k, 0, n}] (* G. C. Greubel, Jan 07 2017 *) CROSSREFS Rows: A000045(j); A000045(j+1), for j > 0; A000032(j), for j > 0; A000285(j-1), for j > 0; A022095(j-1), for j > 0; A022096(j-1), for j > 0; A022097(j-1), for j > 0. Diagonals: a(i, i) = A094588(i); a(i, i+1) = A007502(i+1); a(i, i+2) = A088209(i); Sum[a(i-j, j), {j=0...i}] = A104161(i). a(i, j) = A101220(i, 0, j). Rows 7 - 19: A022098(j-1), for j > 0; A022099(j-1), for j > 0; A022100(j-1), for j > 0; A022101(j-1), for j > 0; A022102(j-1), for j > 0; A022103(j-1), for j > 0; A022104(j-1), for j > 0; A022106(j-1), for j > 0; A022107(j-1), for j > 0; A022108(j-1), for j > 0; A022109(j-1), for j > 0; A022110(j-1), for j > 0. a(2^i-2, j+1) = A118654(i, j), for i > 0. Cf. A117501. Sequence in context: A257654 A167637 A343489 * A220074 A059259 A124394 Adjacent sequences:  A109751 A109752 A109753 * A109755 A109756 A109757 KEYWORD nonn,tabl AUTHOR Ross La Haye, Aug 11 2005; corrected Apr 14 2006 EXTENSIONS More terms from G. C. Greubel, Jan 07 2017 STATUS approved

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Last modified April 18 10:56 EDT 2021. Contains 343087 sequences. (Running on oeis4.)