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%I #9 Aug 12 2015 20:59:14
%S 9,10,11,13,18,30,59,129,299,717,1741,4183,9781,22123,48516,103856,
%T 218683,455839,944616,1950404,4016865,8257883,16962086,34853986,
%U 71735687,148017585,306239910,634872376,1316958592,2728411246
%N a(0) = 9; for n>0, 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 a(0) = 9; binomial transform of sequence gives successive digits of sequence.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p 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: A125004 := proc(nmax) local ldigs,T,diag,row ; T := array(1..nmax,1..nmax) ; ldigs := [9,1,0] ; T[1,1] := ldigs[1] ; for diag from 2 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 > 2 then ldigs := [op(ldigs), op(revert(T[1,diag])) ] ; fi ; od ; RETURN(T) ; end : nmax := 50 : T := A125004(nmax) : for i from 1 to nmax do printf("%d,",T[1,i]) ; od ; # _R. J. Mathar_, Jan 10 2007
%Y Cf. A125588, A125003, A125591.
%K nonn,easy,base
%O 0,1
%A _N. J. A. Sloane_, Jan 08 2007
%E More terms from _R. J. Mathar_, Jan 10 2007
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