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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 A117915. - 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.

Sequence in context: A297323 A257654 A167637 * 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 January 20 17:36 EST 2018. Contains 297961 sequences.