A178873 Partial sums of round(5^n/7).
0, 1, 5, 23, 112, 558, 2790, 13951, 69755, 348773, 1743862, 8719308, 43596540, 217982701, 1089913505, 5449567523, 27247837612, 136239188058, 681195940290, 3405979701451, 17029898507255, 85149492536273
Offset: 0
Examples
a(6) = 0 + 1 + 4 + 18 + 89 + 446 + 2232 = 2790.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..160
- Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
- Index entries for linear recurrences with constant coefficients, signature (7,-12,11,-5).
Programs
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Magma
[Floor((5*5^n+19)/28): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
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Maple
A178873 := proc(n) add( round(5^i/7),i=0..n) ; end proc:
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Mathematica
Accumulate[Round[5^Range[0,25]/7]] (* Harvey P. Dale, Feb 01 2011 *)
Formula
a(n) = round((5*5^n + 7)/28).
a(n) = floor((5*5^n + 19)/28).
a(n) = ceiling((5*5^n - 5)/28).
a(n) = a(n-6) + 558*5^(n-5), n>5.
a(n) = 5*a(n-1) + a(n-6) - 5*a(n-7), n>6.
a(n) = 7*a(n-1) - 12*a(n-2) + 11*a(n-3) - 5*a(n-4), n>3.
G.f.: -(2*x^2-x)/((x-1)*(5*x-1)*(x^2-x+1)).
a(n) = 5^(n+1)/28 + 1/4 + A117373(n+2)/7 = (5*5^n+7)/28 - ((9-i*sqrt(3))*(1-i*sqrt(3))^n + (9+i*sqrt(3))*(1+i*sqrt(3))^n) / (42*2^n) where i is the imaginary unit. - Bruno Berselli, Jan 12 2011