login
Beginning with 1, sum of all possible strings obtained as concatenation of previous (successive) terms.
2

%I #8 Aug 08 2015 19:53:08

%S 1,1,13,1252,12396260,1239500874377560,

%T 12395008619813008676506120642920,

%U 1239500861981300743700524626536099160068958504069412048965143360,12395008619813007437005246265360867650603386910607355428445004411155507757831706693304721638824892440620626536624708440686290240

%N Beginning with 1, sum of all possible strings obtained as concatenation of previous (successive) terms.

%C a(n) is the sum of n(n+1)/2 such strings. a(n) has roughly 2^(n-1) decimal digits. - _R. J. Mathar_, Jul 26 2007

%e a(0) = 1 hence a(1) = 1, a(2) = (1)+(1)+ (11) = 13, a(3) = (1) +(1) +(13) + (11) + (113) + (1113) = 1252.

%p A055642 := proc(n) if n <= 1 then 1 ; else ilog10(n)+ 1; fi ; end: Lcat := proc(L,i,j) local resul,k ; resul := 0 ; for k in op(i..j,L) do resul := resul*10^A055642(k)+k ; od ; RETURN(resul) ; end: A091781 := proc(nmax) local a,anxt,n,i,j; a := [1] ; for n from 1 to nmax do anxt := 0 ; for i from 1 to nops(a) do for j from i to nops(a) do anxt := anxt+Lcat(a,i,j) : od ; od ; a := [op(a),anxt] ; od; RETURN(a) ; end: A091781(9) ; # _R. J. Mathar_, Jul 26 2007

%Y Cf. A091782.

%K base,nonn

%O 0,3

%A _Amarnath Murthy_, Feb 17 2004

%E a(4) and a(5) from Donald Sampson (marsquo(AT)hotmail.com), Sep 17 2004

%E More terms from _R. J. Mathar_, Jul 26 2007