OFFSET
1,3
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,-8,8,-7,3).
FORMULA
a(n) = round((3*3^n - 5*n - 5)/10).
a(n) = floor((3*3^n - 5*n - 3)/10).
a(n) = ceiling((3*3^n - 5*n - 7)/10).
a(n) = round((3*3^n - 5*n - 3)/10).
a(n) = a(n-4) + 8*3^(n-3) - 2, n > 4.
a(n) = 5*a(n-1) - 8*a(n-2) + 8*a(n-3) - 7*a(n-4) + 3*a(n-5), n > 5.
G.f.: x^2*(1+x) / ( (1-3*x)*(1+x^2)*(1-x)^2 ).
EXAMPLE
a(5) = 0 + 1 + 5 + 16 + 48 = 70.
MAPLE
A178706 := proc(n) add( floor(3^i/5), i=0..n) ; end proc:
MATHEMATICA
Table[Floor[(3^(n+1)-5*n-3)/10], {n, 1, 30}] (* G. C. Greubel, Jan 25 2019 *)
PROG
(Magma) [Round((3*3^n-5*n-5)/10): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(30, n, ((3^(n+1)-5*n-3)/10)\1) \\ G. C. Greubel, Jan 25 2019
(Sage) [floor((3^(n+1)-5*n-3)/10) for n in (1..30)] # G. C. Greubel, Jan 25 2019
CROSSREFS
KEYWORD
nonn,less
AUTHOR
Mircea Merca, Dec 26 2010
STATUS
approved