A178577 Partial sums of round(5^n/9).

0, 1, 4, 18, 87, 434, 2170, 10851, 54254, 271268, 1356337, 6781684, 33908420, 169542101, 847710504, 4238552518, 21192762587, 105963812934, 529819064670, 2649095323351, 13245476616754, 66227383083768, 331136915418837

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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 (6,-5,-1,6,-5).

Formula

a(n) = round((5*5^n + 9)/36).

a(n) = floor((5*5^n + 23)/36).

a(n) = ceiling((5*5^n - 5)/36).

a(n) = a(n-6) + 434*5^(n-5), n > 5.

a(n) = 6*a(n-1) - 5*a(n-2) - a(n-3) + 6*a(n-4) - 5*a(n-5), n > 4.

G.f.: (-x^3 - 2*x^2 + x)/((x-1)*(x+1)*(5*x-1)*(x^2-x+1)).

a(n) = 5^(n+1)/36 - (-1)^n/18 + 1/4 - A010892(n+1)/3. - R. J. Mathar, Jan 08 2011

Example

a(6) = 0 + 1 + 3 + 14 + 69 + 347 + 1736 = 2170.

Maple

A178577 := proc(n) add( round(5^i/9), i=0..n) ; end proc:

Mathematica

Table[Round[(5^(n+1) + 9)/36], {n, 0, 40}] (* G. C. Greubel, Jan 30 2019 *)

Prog

(Magma) [Round((5*5^n+9)/36): n in [0..40]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(40, n, n--; round((5^(n+1) + 9)/36)) \\ G. C. Greubel, Jan 30 2019
(Sage) [round((5^(n+1) + 9)/36) for n in (0..40)] # G. C. Greubel, Jan 30 2019

Crossrefs

Sequence in context: A225887 A153294 A164045 * A130524 A298646 A199309

Adjacent sequences: A178574 A178575 A178576 * A178578 A178579 A178580

Keyword

nonn,less

Author

Mircea Merca, Dec 28 2010

Status

approved