A332919 a(n) is the sum of the sums of squared digits of all n-digit numbers.
285, 5415, 79800, 1054500, 13110000, 156750000, 1824000000, 20805000000, 233700000000, 2593500000000, 28500000000000, 310650000000000, 3363000000000000, 36195000000000000, 387600000000000000, 4132500000000000000, 43890000000000000000, 464550000000000000000, 4902000000000000000000
Offset: 1
Examples
a(1) = Sum_{k=1..9} k^2 = A000330(9) = 285.
Links
- Colin Barker, Table of n, a(n) for n = 1..950
- Index entries for linear recurrences with constant coefficients, signature (20,-100).
Programs
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PARI
for(d=1,8, print1(sum(k=10^(d-1), 10^d-1, digits(k)*digits(k)~), ", "))
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PARI
Vec(285*x*(1 - x) / (1 - 10*x)^2 + O(x^40)) \\ Colin Barker, Mar 06 2020
Formula
a(n) = Sum_{k=10^(n-1)..10^n-1} A003132(k).
From Colin Barker, Mar 06 2020: (Start)
G.f.: 285*x*(1 - x) / (1 - 10*x)^2.
a(n) = 20*a(n-1) - 100*a(n-2) for n > 2.
a(n) = 57*2^(n-2) * 5^(n-1) * (1+9*n).
(End)
E.g.f.: (57/20)*(exp(10*x)*(1 + 90*x) - 1). - Stefano Spezia, Mar 06 2020
Extensions
More terms from Colin Barker, Mar 06 2020