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A156002
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Partial sums of round(7^n/9).
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1
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0, 1, 6, 44, 311, 2178, 15250, 106755, 747288, 5231022, 36617161, 256320132, 1794240932, 12559686533, 87917805738, 615424640176, 4307972481243, 30155807368710, 211090651580982, 1477634561066887, 10343441927468220
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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
| a(n)=round((7*7^n-6*n+2)/54) = round((7*7^n-6*n-7)/54).
a(n)=floor((7*7^n-6*n+11)/54).
a(n)=ceil((7*7^n-6*n-7)/54).
a(n)=a(n-3)+(19*7^(n-2)-1)/3, n>2.
a(n)=8*a(n-1)-7*a(n-2)+a(n-3)-8*a(n-4)+7*a(n-5), n>4.
G.f.: -x*(1-2*x+3*x^2) / ( (7*x-1)*(1+x+x^2)*(x-1)^2 ).
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EXAMPLE
| a(3)=0+1+5+38=44.
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MAPLE
| A156002 := proc(n) add( round(7^i/9), i=0..n) ; end proc:
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PROG
| (MAGMA) [Floor((7*7^n-6*n+11)/54): n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
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CROSSREFS
| Cf. A178826.
Sequence in context: A075337 A000561 A091162 * A091163 A189800 A102591
Adjacent sequences: A155999 A156000 A156001 * A156003 A156004 A156005
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KEYWORD
| nonn,less
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AUTHOR
| Mircea Merca (mircea.merca(AT)profinfo.edu.ro), Dec 28 2010
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