Search: id:A125003
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%I A125003
%S A125003 0,5,11,19,31,59,137,337,795,1767,3759,7813,16097,33075,67793,138347,
%T A125003 280677,566041,1136129,2274529,4554047,9143516,18450225,37464726,
%U A125003 76561127,157278265,324136399,668557741,1376893670,2826272837
%N A125003 a(0) = 0, a(1) = 5; for n>1, a(n) is determined by the rule that the 
               concatenation of the leading terms of the difference triangle is 
               the same as the concatenation of the digits of the sequence.
%C A125003 a(0) = 0, a(1) = 5; binomial transform of sequence gives successive digits 
               of sequence.
%H A125003 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%e A125003 Triangle of successive differences begins:
%e A125003 0...5...11...19....31....59....137...337...795....
%e A125003 ..5...6....8....12....28....78....200...458
%e A125003 ....1....2....4....16....50....122...258
%e A125003 ......1....2....12....34....72....136
%e A125003 .........1...10....22....38....64
%e A125003 ...........9....12....16....26
%e A125003 ..............3.....4....10
%e A125003 .................1.....6
%e A125003 ....................5
%p A125003 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 (mathar(AT)strw.leidenuniv.nl), 
               Jan 10 2007
%Y A125003 Cf. A125588, A125004, A125591.
%Y A125003 Sequence in context: A079850 A065995 A023245 this_sequence A062718 A105914 
               A106016
%Y A125003 Adjacent sequences: A125000 A125001 A125002 this_sequence A125004 A125005 
               A125006
%K A125003 nonn,easy,base
%O A125003 0,2
%A A125003 Eric Angelini (Eric.Angelini(AT)kntv.be), Jan 06 2007
%E A125003 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 10 2007

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