OFFSET
0,2
COMMENTS
a(0) = 0, a(1) = 5; binomial transform of sequence gives successive digits of sequence.
LINKS
N. J. A. Sloane, Transforms
EXAMPLE
Triangle of successive differences begins:
0...5...11...19....31....59....137...337...795....
..5...6....8....12....28....78....200...458
....1....2....4....16....50....122...258
......1....2....12....34....72....136
.........1...10....22....38....64
...........9....12....16....26
..............3.....4....10
.................1.....6
....................5
MAPLE
revert := proc(n) local Linv, i, L ; L := convert(n, base, 10) ; Linv := [] ; for i from 1 to nops(L) do Linv := [op(Linv), op(-i, L)] ; od ; RETURN(Linv) ; end: A125003 := proc(nmax) local ldigs, T, diag, row ; T := array(1..nmax, 1..nmax) ; ldigs := [0, 5, 1, 1] ; T[1, 1] := ldigs[1] ; T[1, 2] := ldigs[2] ; T[2, 1] := ldigs[2] ; for diag from 3 to nmax do T[diag, 1] := ldigs[diag] ; for row from diag-1 to 1 by -1 do T[row, diag-row+1] := T[row, diag-row]+T[row+1, diag-row] ; od ; if diag > 3 then ldigs := [op(ldigs), op(revert(T[1, diag])) ] ; fi ; od ; RETURN(T) ; end : nmax := 50 : T := A125003(nmax) : for i from 1 to nmax do printf("%d, ", T[1, i]) ; od ; # R. J. Mathar, Jan 10 2007
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Eric Angelini, Jan 06 2007
EXTENSIONS
More terms from R. J. Mathar, Jan 10 2007
STATUS
approved