A178681 a(n) = 6^n + 6.

7, 12, 42, 222, 1302, 7782, 46662, 279942, 1679622, 10077702, 60466182, 362797062, 2176782342, 13060694022, 78364164102, 470184984582, 2821109907462, 16926659444742, 101559956668422, 609359740010502

Offset: 0

Author

Vincenzo Librandi, Dec 25 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Cf. A000400, A052934 (first differences).

Programs

GAP

List([0..25], n -> 6^n + 6); # G. C. Greubel, Jan 26 2019

Magma

[ 6^n+6: n in [0..25] ];

Mathematica

LinearRecurrence[{7,-6},{7,12},41] (* or *) 6^Range[0,40]+6 (* Harvey P. Dale, Aug 11 2011 *)

PARI

for(n=0,25,print1(6^n+6,",")) \\ Edward Jiang, Nov 22 2013

Sage

[6^n +6 for n in range(25)] # G. C. Greubel, Jan 26 2019

Formula

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

a(n) = 7*a(n-1) - 6*a(n-2).

a(n) = 6*A062394(n-1), n > 0.

G.f.: (7-37*x)/((1-x)*(1-6*x)). - Klaus Brockhaus, Dec 27 2010

a(n) = A000400(n) + 6. - Michel Marcus, Nov 23 2013

E.g.f.: exp(6*x) + 6*exp(x). - G. C. Greubel, Jan 26 2019