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A177881 Partial sums of round(3^n/10). 1
0, 0, 1, 4, 12, 36, 109, 328, 984, 2952, 8857, 26572, 79716, 239148, 717445, 2152336, 6457008, 19371024, 58113073, 174339220, 523017660, 1569052980, 4707158941, 14121476824, 42364430472, 127093291416 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..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 (4,-4,4,-3).

FORMULA

a(n) = round((3*3^n-3)/20) = round((3*3^n-5)/20).

a(n) = floor((3*3^n-1)/20).

a(n) = ceiling((3*3^n-9)/20).

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

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

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

EXAMPLE

a(4) = 0 + 0 + 1 + 3 + 8 = 12.

MAPLE

A177881 := proc(n) add( round(3^i/10), i=0..n) ; end proc:

PROG

(MAGMA) [Round((3*3^n-3)/20): n in [0..30]]; // Vincenzo Librandi, Jun 23 2011

(PARI) a(n)=(3^(n+1)-1)\20 \\ Charles R Greathouse IV, Jun 23 2011

CROSSREFS

Cf. A015577 (bisection of round(3^n/10)).

Sequence in context: A170589 A170637 A170685 * A290899 A290905 A000781

Adjacent sequences:  A177878 A177879 A177880 * A177882 A177883 A177884

KEYWORD

nonn,less,easy

AUTHOR

Mircea Merca, Dec 28 2010

STATUS

approved

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Last modified February 20 21:07 EST 2019. Contains 320347 sequences. (Running on oeis4.)