A291658 a(n) is the sum of all integers from 5^n to 5^(n+1)-1.

10, 290, 7450, 187250, 4686250, 117181250, 2929656250, 73242031250, 1831053906250, 45776363281250, 1144409160156250, 28610229394531250, 715255736816406250, 17881393430175781250, 447034835803222656250, 11175870895324707031250, 279396772384338378906250

Offset

0,1

Comments

a(n) is the sum of all (positive) numbers having exactly (n+1) digits when written in base 5. - Alois P. Heinz, Sep 25 2017

Links

Colin Barker, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (30,-125).

Formula

a(n) = ((5^n)/2)*(5^(n+2) - 5^n - 4), n >= 0.

From Colin Barker, Sep 12 2017: (Start)

G.f.: 10*(1 - x) / ((1 - 5*x)*(1 - 25*x)).

a(n) = 30*a(n-1) - 125*a(n-2) for n>1.

(End)

a(n) = A162729(n+1) - A162729(n). - Alois P. Heinz, Sep 25 2017

Example

For n=0, the sum is from 1 to 4, so a(0)=10;
for n=1, the sum is from 5 to 24, so a(1)=290, etc.

Maple

a:= unapply(sum(i, i=5^n..5^(n+1)-1), n):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 25 2017

Prog

(PARI) Vec(10*(1 - x) / ((1 - 5*x)*(1 - 25*x)) + O(x^30)) \\ Colin Barker, Sep 12 2017

Crossrefs

Cf. A010036, A226508, A121544, A101291, A162729.

Sequence in context: A049387 A222672 A024295 * A159960 A258794 A239775

Adjacent sequences: A291655 A291656 A291657 * A291659 A291660 A291661

Keyword

nonn,easy

Author

Enrique Navarrete, Aug 28 2017

Status

approved