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A125608
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Triangle read by rows: given the left border = the Lucas numbers, (1, 3, 4, 7...), T(n,k) = (n-1,k) + (n-1,k-1).
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1
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1, 3, 1, 4, 4, 1, 7, 8, 5, 1, 11, 15, 13, 6, 1, 18, 26, 28, 19, 7, 1, 29, 44, 54, 47, 26, 8, 1, 47, 73, 98, 101, 73, 34, 9, 1, 76, 120, 171, 199, 174, 107, 43, 10, 1, 123, 196, 291, 370, 373, 281, 150, 53, 11, 1, 199, 319, 487, 661, 743, 654, 431, 203, 64, 12, 1, 322, 518, 806
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = A027973: (1, 4, 9, 21, 46, 99, 209...)
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EXAMPLE
| First few rows of the triangle are:
1;
3, 1;
4, 4, 1;
7, 8, 5, 1;
11, 15, 13, 6, 1;
18, 26, 28, 19, 7, 1;
...
(6,3) = 28 = 13 + 15 = (5,3) + (5,2).
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MAPLE
| L[1]:=1: L[2]:=3: for n from 3 to 12 do L[n]:=L[n-1]+L[n-2] od: T:=proc(n, k) if k=1 then L[n] elif n=1 then 0 else T(n-1, k)+T(n-1, k-1) fi end: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 01 2007
A000204 := proc(n) if n =1 then RETURN(1) ; elif n = 2 then RETURN(3) ; else RETURN( A000204(n-1)+A000204(n-2)) ; fi ; end ; A125608 := proc(nmax) local a, row, col, anext ; a := [1] ; row := 1 ; while nops(a) < nmax do row := row+1 ; a := [op(a), A000204(row)] ; for col from 2 to row-1 do anext := op(-row, a)+op(-row+1, a) ; a := [op(a), anext] ; od ; a := [op(a), 1] ; od ; RETURN(a) ; end ; A125608(80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2007
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CROSSREFS
| Cf. A027973.
Sequence in context: A054907 A089554 A129246 * A099813 A141300 A014388
Adjacent sequences: A125605 A125606 A125607 * A125609 A125610 A125611
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 27 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 01 2007
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2007
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