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

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..950

Index entries for linear recurrences with constant coefficients, signature (20,-100).

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

Example

a(1) = Sum_{k=1..9} k^2 = A000330(9) = 285.

Prog

(PARI) for(d=1, 8, print1(sum(k=10^(d-1), 10^d-1, digits(k)*digits(k)~), ", "))
(PARI) Vec(285*x*(1 - x) / (1 - 10*x)^2 + O(x^40)) \\ Colin Barker, Mar 06 2020

Crossrefs

Cf. A003132, A333034.

Sequence in context: A209311 A176712 A225881 * A278629 A241970 A231422

Adjacent sequences: A332916 A332917 A332918 * A332920 A332921 A332922

Keyword

nonn,base,easy

Author

Hugo Pfoertner, Mar 06 2020

Extensions

More terms from Colin Barker, Mar 06 2020

Status

approved