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A332919 a(n) is the sum of the sums of squared digits of all n-digit numbers.

%I A332919 #21 Mar 14 2020 13:15:41
%S A332919 285,5415,79800,1054500,13110000,156750000,1824000000,20805000000,
%T A332919 233700000000,2593500000000,28500000000000,310650000000000,
%U A332919 3363000000000000,36195000000000000,387600000000000000,4132500000000000000,43890000000000000000,464550000000000000000,4902000000000000000000
%N A332919 a(n) is the sum of the sums of squared digits of all n-digit numbers.
%H A332919 Colin Barker, <a href="/A332919/b332919.txt">Table of n, a(n) for n = 1..950</a>
%H A332919 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).
%F A332919 a(n) = Sum_{k=10^(n-1)..10^n-1} A003132(k).
%F A332919 From _Colin Barker_, Mar 06 2020: (Start)
%F A332919 G.f.: 285*x*(1 - x) / (1 - 10*x)^2.
%F A332919 a(n) = 20*a(n-1) - 100*a(n-2) for n > 2.
%F A332919 a(n) = 57*2^(n-2) * 5^(n-1) * (1+9*n).
%F A332919 (End)
%F A332919 E.g.f.: (57/20)*(exp(10*x)*(1 + 90*x) - 1). - _Stefano Spezia_, Mar 06 2020
%e A332919 a(1) = Sum_{k=1..9} k^2 = A000330(9) = 285.
%o A332919 (PARI) for(d=1,8, print1(sum(k=10^(d-1), 10^d-1, digits(k)*digits(k)~), ", "))
%o A332919 (PARI) Vec(285*x*(1 - x) / (1 - 10*x)^2 + O(x^40)) \\ _Colin Barker_, Mar 06 2020
%Y A332919 Cf. A003132, A333034.
%K A332919 nonn,base,easy
%O A332919 1,1
%A A332919 _Hugo Pfoertner_, Mar 06 2020
%E A332919 More terms from _Colin Barker_, Mar 06 2020