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

0,3

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).

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

Example

a(6) = 0 + 1 + 4 + 18 + 89 + 446 + 2232 = 2790.

Maple

A178873 := proc(n) add( round(5^i/7), i=0..n) ; end proc:

Mathematica

Accumulate[Round[5^Range[0, 25]/7]] (* Harvey P. Dale, Feb 01 2011 *)

Prog

(Magma) [Floor((5*5^n+19)/28): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

Crossrefs

Sequence in context: A244936 A017975 A360100 * A186652 A199312 A320326

Adjacent sequences: A178870 A178871 A178872 * A178874 A178875 A178876

Keyword

nonn,less

Author

Mircea Merca, Dec 28 2010

Status

approved