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

Author

Mircea Merca, Dec 26 2010

Keywords

• nonn
• less

Comments

Partial sums of A037521.

Examples

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

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).

Crossrefs

Cf. A037521.

Programs

Magma

[Round((8*4^n-14*n-13)/42): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011

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 *)

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

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 ).