OFFSET
1,2
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 (9,-16,16,-15,7).
FORMULA
a(n) = round((7*7^n - 30*n - 25)/60)/2.
a(n) = floor((7*7^n - 30*n - 7)/60)/2.
a(n) = ceiling((7*7^n - 30*n - 43)/60)/2.
a(n) = a(n-4) + 20*7^(n-3) - 1 , n > 4.
From Bruno Berselli, Dec 27 2010: (Start)
a(n) = (7^(n+1) - 30*n + 6*(2+(-1)^n)*(-1)^((2*n-1+(-1)^n)/4)-25)/120.
G.f.: x^2*(2+x)/((1-7*x)*(1+x^2)*(1-x)^2). (End)
EXAMPLE
a(3) = (1/2)*(floor(7/10) + floor(49/10) + floor(343/10))
= (1/2)*(0 + 4 + 34) = (1/2)*38 = 19.
MAPLE
seq(1/2*floor((7*7^n-30*n-7)/60), n=1..25);
MATHEMATICA
CoefficientList[Series[x(2+x)/((1-7x)(1+x^2)(1-x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
PROG
(Magma) [(1/2*Floor((7*7^n-30*n-7)/60)): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) my(x='x+O('x^30)); concat([0], Vec(x^2*(2+x)/((1-7*x)*(1+x^2)*(1-x)^2))) \\ G. C. Greubel, Jan 22 2019
(Sage) a=(x^2*(2+x)/((1-7*x)*(1+x^2)*(1-x)^2)).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jan 22 2019
(GAP) a:=List([1..25], n->(1/2)*Int((7*7^n-30*n-7)/60));; Print(a); # Muniru A Asiru, Jan 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Dec 27 2010
STATUS
approved