OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
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 (7,-11,4,7,-11,5).
FORMULA
a(n) = round((5*5^n - 18*n - 18)/36).
a(n) = floor((5*5^n - 18*n - 5)/36).
a(n) = ceiling((5*5^n - 18*n - 31)/36).
a(n) = a(n-6) + 434*5^(n-5) - 3, n > 6.
a(n) = 7*a(n-1) - 11*a(n-2) + 4*a(n-3) + 7*a(n-4) - 11*a(n-5) + 5*a(n-6), n > 5.
G.f.: x^2*(2 + x + x^2) / ( (1-5*x)*(1+x)*(1-x+x^2)*(1-x)^2 ).
EXAMPLE
a(7) = 0 + 2 + 13 + 69 + 347 + 1736 + 8680 = 10847.
MAPLE
A178750 := proc(n) add( floor(5^i/9), i=0..n) ; end proc:
MATHEMATICA
Accumulate[Floor[5^Range[0, 30]/9]] (* Harvey P. Dale, Sep 19 2011 *)
PROG
(Magma) [Round((5*5^n-18*n-18)/36): n in [0..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(30, n, n--; ((5*5^n - 18*n - 5)/36)\1) \\ G. C. Greubel, Jan 24 2019
(Sage) [floor((5*5^n - 18*n - 5)/36) for n in (0..30)] # G. C. Greubel, Jan 24 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Mircea Merca, Dec 26 2010
STATUS
approved