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A178459 Partial sums of floor(2^n/31). 1
0, 0, 0, 0, 1, 3, 7, 15, 31, 64, 130, 262, 526, 1054, 2111, 4225, 8453, 16909, 33821, 67646, 135296, 270596, 541196, 1082396, 2164797, 4329599, 8659203, 17318411, 34636827, 69273660, 138547326, 277094658, 554189322, 1108378650, 2216757307, 4433514621, 8867029249, 17734058505, 35468117017, 70936234042 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Partial sums of A119610(n-4).

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 (3,-2,0,0,1,-3,2).

FORMULA

a(n) = round((10*2^n - 31*n - 7)/155).

a(n) = floor((10*2^n - 31*n + 22)/155).

a(n) = ceiling((10*2^n - 31*n - 36)/155).

a(n) = round((10*2^n - 31*n - 10)/155).

a(n) = a(n-5) + 2^(n-4) - 1, n > 4,

G.f.: -x^5/((x-1)^2*(2*x-1)*(x^4 + x^3 + x^2 + x + 1)). [Colin Barker, Oct 27 2012]

EXAMPLE

a(29) = 0 + 0 + 0 + 0 + 1 + 2 + 4 + 8 + 16 + 33 + 66 + 132 + 264 + 528 + 1057 + 2114 + 4228 + 8456 + 16912 + 33825 + 67650 + 135300 + 270600 + 541200 + 1082401 + 2164802 + 4329604 + 8659208 + 17318416 = 34636827.

MAPLE

seq(round((10*2^n-31*n-7)/155), n=1..32)

MATHEMATICA

Floor[2^Range[40]/31]//Accumulate (* Harvey P. Dale, May 11 2018 *)

PROG

(Magma) [Round((10*2^n-31*n-7)/155): n in [1..40]]; // Vincenzo Librandi, Jun 21 2011

CROSSREFS

Cf. A119610.

Sequence in context: A174743 A146686 A309172 * A129984 A351707 A146811

Adjacent sequences: A178456 A178457 A178458 * A178460 A178461 A178462

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Dec 22 2010

STATUS

approved

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Last modified November 28 02:51 EST 2022. Contains 358406 sequences. (Running on oeis4.)