A178711 Partial sums of floor(5^n/7).

0, 3, 20, 109, 555, 2787, 13947, 69750, 348767, 1743856, 8719302, 43596534, 217982694, 1089913497, 5449567514, 27247837603, 136239188049, 681195940281, 3405979701441, 17029898507244, 85149492536261, 425747462681350, 2128737313406796, 10643686567034028, 53218432835170188

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..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 (7,-11,4,7,-11,5).

Formula

a(n) = round((5*5^n - 14*n - 14)/28).

a(n) = floor((5*5^n - 14*n - 5)/28).

a(n) = ceiling((5*5^n - 14*n - 23)/28).

a(n) = a(n-6) + 558*5^(n-5) - 3, n > 6.

G.f.: -x^2*(2*x^2 - x + 3)/((x-1)^2*(x+1)*(5*x-1)*(x^2-x+1)). [Colin Barker, Oct 27 2012]

Example

a(7) = 0 + 3 + 17 + 89 + 446 + 2232 + 11160 = 13947.

Maple

seq(floor((5*5^n-14*n-5)/28), n=1..25)

Mathematica

Accumulate[Floor[5^Range[30]/7]] (* or *) LinearRecurrence[{7, -11, 4, 7, -11, 5}, {0, 3, 20, 109, 555, 2787}, 30] (* Harvey P. Dale, May 27 2018 *)

Prog

(Magma) [Round((5*5^n-14*n-14)/28): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(30, n, ((5^(n+1)-14*n-5)/28)\1) \\ G. C. Greubel, Jan 24 2019
(Sage) [floor((5^(n+1)-14*n-5)/28) for n in (1..30)] # G. C. Greubel, Jan 24 2019

Crossrefs

Sequence in context: A158243 A139471 A154641 * A257067 A108911 A005096

Adjacent sequences: A178708 A178709 A178710 * A178712 A178713 A178714

Keyword

nonn,easy

Author

Mircea Merca, Dec 26 2010

Status

approved