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A125608
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).
1
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
OFFSET
1,2
COMMENTS
Row sums = A027973: (1, 4, 9, 21, 46, 99, 209, ...).
EXAMPLE
First few rows of the triangle:
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).
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, 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, Jan 07 2007
CROSSREFS
Cf. A027973.
Sequence in context: A246354 A286625 A129246 * A182001 A099813 A376782
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 27 2006
EXTENSIONS
More terms from Emeric Deutsch, Jan 01 2007
More terms from R. J. Mathar, Jan 07 2007
STATUS
approved