A178826 Partial sums of floor(7^n/9).

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

Offset

1,2

Links

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

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 (8,-7,1,-8,7).

Formula

a(n) = round((7*7^n - 24*n - 16)/54).

a(n) = floor((7*7^n - 24*n - 7)/54).

a(n) = ceiling((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) / ( (1-7*x)*(1+x+x^2)*(1-x)^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+3x)/((1-7x)(1+x+x^2)(1-x)^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
(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(5+3*x)/((1-7*x)*(1-x)*(1-x^3)))) \\ G. C. Greubel, Jan 22 2019
(Sage) (x*(5+3*x)/((1-7*x)*(1-x)*(1-x^3))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 22 2019
(GAP) a:=[0, 5, 43, 309, 2176];; for n in [6..30] do a[n]:=8*a[n-1]-7*a[n-2]+a[n-3]-8*a[n-4]+7*a[n-5]; od; a; # G. C. Greubel, Jan 22 2019

Crossrefs

Sequence in context: A317282 A182191 A038140 * A082311 A269121 A326884

Adjacent sequences: A178823 A178824 A178825 * A178827 A178828 A178829

Keyword

nonn,less

Author

Mircea Merca, Dec 27 2010

Status

approved