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A178873
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Partial sums of round(5^n/7).
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1
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0, 1, 5, 23, 112, 558, 2790, 13951, 69755, 348773, 1743862, 8719308, 43596540, 217982701, 1089913505, 5449567523, 27247837612, 136239188058, 681195940290, 3405979701451, 17029898507255, 85149492536273
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..160
Index to sequences with linear recurrences with constant coefficients, signature (7,-12,11,-5).
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
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FORMULA
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a(n)=round((5*5^n+7)/28).
a(n)=floor((5*5^n+19)/28).
a(n)=ceil((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
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EXAMPLE
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a(6)=0+1+4+18+89+446+2232=2790.
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MAPLE
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A178873 := proc(n) add( round(5^i/7), i=0..n) ; end proc:
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MATHEMATICA
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Accumulate[Round[5^Range[0, 25]/7]] [From Harvey P. Dale, Feb. 1, 2011]
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PROG
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(MAGMA) [Floor((5*5^n+19)/28): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
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CROSSREFS
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Sequence in context: A017974 A017975 A186652 * A199312 A113284 A104090
Adjacent sequences: A178870 A178871 A178872 * A178874 A178875 A178876
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KEYWORD
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nonn,less
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AUTHOR
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Mircea Merca, Dec 28 2010
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STATUS
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approved
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