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A178826
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Partial sums of floor(7^n/9).
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2
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0, 5, 43, 309, 2176, 15248, 106752, 747285, 5231019, 36617157, 256320128, 1794240928, 12559686528, 87917805733, 615424640171, 4307972481237, 30155807368704, 211090651580976, 1477634561066880, 10343441927468213, 72404093492277547, 506828654445942885, 3547800581121600256, 24834604067851201856, 173842228474958413056
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OFFSET
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1,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..400
Index to sequences with linear recurrences with constant coefficients, signature (8,-7,1,-8,7).
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((7*7^n-24*n-16)/54).
a(n)=floor((7*7^n-24*n-7)/54).
a(n)=ceil((7*7^n-24*n-25)/54).
a(n)=round((7*7^n-24*n-7)/54).
a(n)=a(n-3)+(19*7^(n-2)-4)/3 , n>3.
a(n)=8*a(n-1)-7*a(n-2)+a(n-3)-8*a(n-4)+7*a(n-5), n>5.
G.f.: -x^2*(5+3*x) / ( (7*x-1)*(1+x+x^2)*(x-1)^2 ).
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EXAMPLE
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a(4)=0+5+38+266=309.
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MAPLE
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A178826 := proc(n) add( floor(7^i/9), i=0..n) ; end proc:
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PROG
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(MAGMA) [Round((7*7^n-24*n-16)/54): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
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CROSSREFS
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(MAGMA) [&+[Floor(7^k/9): k in [1..n]]: n in [1..25]]; // Bruno Berselli, Apr 26 2011
Sequence in context: A221874 A182191 A038140 * A082311 A156886 A112115
Adjacent sequences: A178823 A178824 A178825 * A178827 A178828 A178829
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KEYWORD
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nonn,less
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AUTHOR
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Mircea Merca, Dec 27 2010
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STATUS
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approved
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