A140730 a(4*n)=5^n, a(4*n+1)=2*5^n, a(4*n+2)=3*5^n, a(4*n+3)=4*5^n.

1, 2, 3, 4, 5, 10, 15, 20, 25, 50, 75, 100, 125, 250, 375, 500, 625, 1250, 1875, 2500, 3125, 6250, 9375, 12500, 15625, 31250, 46875, 62500, 78125, 156250, 234375, 312500, 390625, 781250, 1171875, 1562500, 1953125, 3906250, 5859375, 7812500

Offset: 0

Author

Reinhard Zumkeller, May 26 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,5).

Crossrefs

Cf. A000079, A037124, A038754, A133464, A140740.

Programs

Mathematica

Table[(n + 1 - 4 Floor[n/4]) 5^Floor[n/4], {n, 0, 40}] (* Bruno Berselli, Aug 05 2015 *)
LinearRecurrence[{0,0,0,5},{1,2,3,4},40] (* Harvey P. Dale, Jul 01 2022 *)

PARI

a(n)=(n+1-n\4*4)*5^(n\4) \\ Charles R Greathouse IV, Oct 07 2015

Python

def A140730(n): return ((n&3)+1)*5**(n>>2) # Chai Wah Wu, Jan 18 2023

Formula

a(n+1) = a(n) + a(n - n mod 4).

a(n) = A140740(n+4,4).

O.g.f.: (1+2*x+3*x^2+4*x^3)/(1-5*x^4). - R. J. Mathar, May 31 2008

a(n) = (n+1-4*floor(n/4))*5^floor(n/4). - Luce ETIENNE, Aug 05 2015

a(n) = 5*a(n-4) for n>3; a(n) = n+1 for n<5. - Bruno Berselli, Aug 05 2015

Sum_{n>=0} 1/a(n) = 125/48. - Amiram Eldar, Jan 21 2022