A156002 Partial sums of round(7^n/9).

0, 1, 6, 44, 311, 2178, 15250, 106755, 747288, 5231022, 36617161, 256320132, 1794240932, 12559686533, 87917805738, 615424640176, 4307972481243, 30155807368710, 211090651580982, 1477634561066887, 10343441927468220

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for 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 - 6*n + 2)/54) = round((7*7^n - 6*n - 7)/54).

a(n) = floor((7*7^n - 6*n + 11)/54).

a(n) = ceiling((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).

Example

a(3) = 0 + 1 + 5 + 38 = 44.

Maple

A156002 := proc(n) add( round(7^i/9), i=0..n) ; end proc:

Mathematica

CoefficientList[Series[-x*(1 - 2*x + 3*x^2)/((7*x - 1)*(1 + x + x^2)*(x - 1)^2), {x, 0, 40}], x] (* or *)
LinearRecurrence[{8, -7, 1, -8, 7}, {0, 1, 6, 44, 311}, 40] (* Stefano Spezia, Sep 02 2018 *)
Accumulate[Round[7^Range[0, 20]/9]] (* Harvey P. Dale, Apr 24 2021 *)

Prog

(Magma) [Floor((7*7^n-6*n+11)/54): n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Crossrefs

Cf. A178826.

Sequence in context: A309418 A203601 A091162 * A091163 A189800 A227665

Adjacent sequences: A155999 A156000 A156001 * A156003 A156004 A156005

Keyword

nonn,less

Author

Mircea Merca, Dec 28 2010

Status

approved