A178710 Partial sums of floor(4^n/7).

0, 2, 11, 47, 193, 778, 3118, 12480, 49929, 199725, 798911, 3195656, 12782636, 51130558, 204522247, 818089003, 3272356029, 13089424134, 52357696554, 209430786236, 837723144965, 3350892579881, 13403570319547, 53614281278212, 214457125112872

Offset

1,2

Comments

Partial sums of A037521.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..700

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 (5,-4,1,-5,4).

Formula

a(n) = round((8*4^n - 14*n - 13)/42).

a(n) = floor((8*4^n - 14*n - 8)/42).

a(n) = ceiling((8*4^n - 14*n - 18)/42).

a(n) = round((8*4^n - 14*n - 8)/42).

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

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

G.f.: x^2*(2+x)/ ( (1-4*x)*(1+x+x^2)*(1-x)^2 ).

Example

a(4) = 0 + 2 + 9 + 36 = 47.

Maple

A178710 := proc(n) add( floor(4^i/7), i=0..n) ; end proc:

Mathematica

Accumulate[Floor[4^Range[30]/7]] (* or *) LinearRecurrence[{5, -4, 1, -5, 4}, {0, 2, 11, 47, 193}, 30] (* Harvey P. Dale, Aug 15 2015 *)

Prog

(Magma) [Round((8*4^n-14*n-13)/42): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(30, n, ((8*4^n-14*n-8)/42)\1) \\ G. C. Greubel, Jan 25 2019
(Sage) [floor((8*4^n-14*n-8)/42) for n in (1..30)] # G. C. Greubel, Jan 25 2019

Crossrefs

Cf. A037521.

Sequence in context: A089682 A211671 A198693 * A050929 A019005 A112288

Adjacent sequences: A178707 A178708 A178709 * A178711 A178712 A178713

Keyword

nonn,less

Author

Mircea Merca, Dec 26 2010

Status

approved