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
Examples
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.
Links
- Colin Barker, Table of n, a(n) for n = 0..700
- Index entries for linear recurrences with constant coefficients, signature (30,-125).
Programs
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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
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PARI
Vec(10*(1 - x) / ((1 - 5*x)*(1 - 25*x)) + O(x^30)) \\ Colin Barker, Sep 12 2017
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)
Comments