A178750 Partial sums of floor(5^n/9).

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

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