A178829 Partial sums of (1/2)*floor(7^n/10).

0, 2, 19, 139, 979, 6861, 48038, 336278, 2353958, 16477720, 115344057, 807408417, 5651858937, 39563012579, 276941088076, 1938587616556, 13570113315916, 94990793211438, 664935552480095, 4654548867360695

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 (9,-16,16,-15,7).

Formula

a(n) = round((7*7^n - 30*n - 25)/60)/2.

a(n) = floor((7*7^n - 30*n - 7)/60)/2.

a(n) = ceiling((7*7^n - 30*n - 43)/60)/2.

a(n) = a(n-4) + 20*7^(n-3) - 1 , n > 4.

From Bruno Berselli, Dec 27 2010: (Start)

a(n) = (7^(n+1) - 30*n + 6*(2+(-1)^n)*(-1)^((2*n-1+(-1)^n)/4)-25)/120.

G.f.: x^2*(2+x)/((1-7*x)*(1+x^2)*(1-x)^2). (End)

Example

a(3) = (1/2)*(floor(7/10) + floor(49/10) + floor(343/10))
     = (1/2)*(0 + 4 + 34) = (1/2)*38 = 19.

Maple

seq(1/2*floor((7*7^n-30*n-7)/60), n=1..25);

Mathematica

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

Prog

(Magma) [(1/2*Floor((7*7^n-30*n-7)/60)): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) my(x='x+O('x^30)); concat([0], Vec(x^2*(2+x)/((1-7*x)*(1+x^2)*(1-x)^2))) \\ G. C. Greubel, Jan 22 2019
(Sage) a=(x^2*(2+x)/((1-7*x)*(1+x^2)*(1-x)^2)).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jan 22 2019
(GAP) a:=List([1..25], n->(1/2)*Int((7*7^n-30*n-7)/60));; Print(a); # Muniru A Asiru, Jan 22 2019

Crossrefs

Cf. A037754.

Sequence in context: A249690 A206948 A089364 * A166298 A220792 A220957

Adjacent sequences: A178826 A178827 A178828 * A178830 A178831 A178832

Keyword

nonn,easy

Author

Mircea Merca, Dec 27 2010

Status

approved