A132079 a(n) = (5^n + 3)/2.

2, 4, 14, 64, 314, 1564, 7814, 39064, 195314, 976564, 4882814, 24414064, 122070314, 610351564, 3051757814, 15258789064, 76293945314, 381469726564, 1907348632814, 9536743164064, 47683715820314

Offset: 0

Author

Mohit Maheshwari (mohitmahe1989(AT)gmail.com), Oct 30 2007

Keywords

• easy
• nonn

Comments

(5^n + 3)/2 is always divisible by 2 and the next value can be generated by appending 4 at the ones place and adding the rest of the number with the respective power of 5. For example, 314 can be generated after 64 by just writing 4 at the ones place and adding 5^2 to 6 to get 31 and appending 31 to 4 to get 314.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A047850.

Programs

Magma

[(5^n+3)/2: n in [0..30]]; // Vincenzo Librandi, May 02 2011

Mathematica

Table[(5^n + 3)/2, {n, 0, 24}] (* Alonso del Arte, May 02 2011 *)

PARI

a(n)=5^n\2+2 \\ Charles R Greathouse IV, May 02 2011

Formula

From Elmo R. Oliveira, Dec 21 2023: (Start)

a(n) = 2*A047850(n).

a(n) = 5*a(n-1) - 6 for n>0.

a(n) = 6*a(n-1) - 5*a(n-2) for n>1.

G.f.: (2-8*x)/((1-x)*(1-5*x)).

E.g.f.: exp(x)*(exp(4*x) + 3)/2. (End)

Extensions

Offset changed from 4 to 0; corrected and extended by Vincenzo Librandi, May 02 2011