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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

%I

%S 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,

%T 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,

%U 28,37,47,55,55,0,1,10,10,17,23,33,45,60,76,89,89

%N Matrix defined by: a(i,0) = 0, a(i,j) = i*Fibonacci(j-1) + Fibonacci(j), for j > 0; read by antidiagonals.

%C Lower triangular version is at A117915. - _Ross La Haye_, Apr 12 2006

%H G. C. Greubel, <a href="/A109754/b109754.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F 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.

%F G.f.: (x(1+ix))/(1-x-x^2).

%F 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

%e {0};

%e {0,1};

%e {0,1,1};

%e {0,1,2,2};

%e {0,1,3,3,3};

%e {0,1,4,4,5,5};

%e {0,1,5,5,7,8,8}

%t 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 *)

%Y 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).

%Y 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.

%Y a(2^i-2, j+1) = A118654(i, j), for i > 0.

%K nonn,tabl

%O 0,9

%A _Ross La Haye_, Aug 11 2005; corrected Apr 14 2006

%E More terms from _G. C. Greubel_, Jan 07 2017

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Last modified May 30 00:42 EDT 2017. Contains 287304 sequences.