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A178826 Partial sums of floor(7^n/9). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

FORMULA

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 ).

EXAMPLE

a(4)=0+5+38+266=309.

MAPLE

A178826 := proc(n) add( floor(7^i/9), i=0..n) ; end proc:

MATHEMATICA

CoefficientList[Series[- x (5 + 3 x)/((7 x - 1) (1 + x + x^2) (x - 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)

PROG

(MAGMA) [Floor((7*7^n-24*n-7)/54): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011

(MAGMA) [&+[Floor(7^k/9): k in [1..n]]: n in [1..25]]; // Bruno Berselli, Apr 26 2011

CROSSREFS

Sequence in context: A221874 A182191 A038140 * A082311 A241707 A156886

Adjacent sequences:  A178823 A178824 A178825 * A178827 A178828 A178829

KEYWORD

nonn,less

AUTHOR

Mircea Merca, Dec 27 2010

STATUS

approved

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Last modified November 27 00:18 EST 2014. Contains 250152 sequences.