login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178750 Partial sums of floor(5^n/9). 1
0, 0, 2, 15, 84, 431, 2167, 10847, 54249, 271262, 1356331, 6781678, 33908414, 169542094, 847710496, 4238552509, 21192762578, 105963812925, 529819064661, 2649095323341, 13245476616743, 66227383083756, 331136915418825, 1655684577094172, 8278422885470908, 41392114427354588 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A109725 A057152 A002740 * A108475 A328007 A098624

Adjacent sequences:  A178747 A178748 A178749 * A178751 A178752 A178753

KEYWORD

nonn

AUTHOR

Mircea Merca, Dec 26 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)