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%I #8 Jan 24 2016 23:45:19
%S 1,3,6,10,15,21,28,36,45,1,2,4,7,11,16,22,29,37,46,3,4,6,9,13,18,24,
%T 31,39,48,6,7,9,12,16,21,27,34,42,51,10,11,13,16,20,25,31,38,46,55,15,
%U 16,18,21,25,30,36,43,51,60,21,22,24,27,31,36,42,49,57,66,28,29,31,34,38,43,49,56,64,73,36,37,39,42,46,51,57,64,72,81
%N Sum of the triangular numbers whose indices are the digits of n.
%F From _Robert Israel_, Jan 21 2016: (Start)
%F G.f.: A(x) = Sum_{j >= 0} (1-x^(10^j))/((1-x)*(1-x^(10^(j+1)))) * Sum_{d=1..9} d*(d+1)/2 * x^(d*10^j)
%F satisfies A(x) = (1-x^10)*A(x^10)/(1-x) + (1+3*x^2+6*x^3+10*x^4+15*x^5+21*x^6+28*x^7+36*x^8+45*x^9)/(1-x^10).
%F a(10*m + j) = a(m) + j*(j+1)/2 for 0 <= j <= 9. (End)
%e a(12) = 1*2/2 + 2*3/2 = 4.
%p seq(add(d*(d+1)/2, d = convert(n,base,10)), n=1..1000); # _Robert Israel_, Jan 21 2016
%t f[n_]:=Total[IntegerDigits[n]*(IntegerDigits[n]+1)/2];f/@Range@100
%o (PARI) a(n) = {my(d = digits(n)); sum(k=1, #d, d[k]*(d[k]+1)/2);} \\ _Michel Marcus_, Jan 12 2016
%Y Cf. A000217, A266998, A266999.
%K base,easy,nonn
%O 1,2
%A _Ivan N. Ianakiev_, Jan 12 2016
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