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Search: id:A109754
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| A109754 |
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Matrix defined by: a(i,0) = 0, a(i,j) = i*Fibonacci[j-1] + Fibonacci[j], for j > 0; read by antidiagonals. |
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28
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| 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
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Lower triangular version is at A117915. - Ross La Haye (rlahaye(AT)new.rr.com), Apr 12 2006
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FORMULA
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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[a(i-j+1, j), {j, 0, i+1}] - Sum[a(i-j, j), {j, 0, i}] = A001595(i). - Ross La Haye (rlahaye(AT)new.rr.com), Jun 03 2006
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EXAMPLE
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{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}
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CROSSREFS
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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: A000209 A104245 A167637 this_sequence A059259 A124394 A086460
Adjacent sequences: A109751 A109752 A109753 this_sequence A109755 A109756 A109757
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KEYWORD
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nonn,tabl
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Aug 11 2005; corrected Apr 14 2006
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