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

0,1

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).

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)

Mathematica

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

Prog

(Magma) [(5^n+3)/2: n in [0..30]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=5^n\2+2 \\ Charles R Greathouse IV, May 02, 2011

Crossrefs

Cf. A047850.

Sequence in context: A089127 A132852 A352644 * A055790 A322623 A245139

Adjacent sequences: A132076 A132077 A132078 * A132080 A132081 A132082

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved