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A062394 a(n) = 6^n + 1. 42
2, 7, 37, 217, 1297, 7777, 46657, 279937, 1679617, 10077697, 60466177, 362797057, 2176782337, 13060694017, 78364164097, 470184984577, 2821109907457, 16926659444737, 101559956668417, 609359740010497, 3656158440062977 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..150

Index entries for linear recurrences with constant coefficients, signature (7,-6).

FORMULA

a(n) = 6*a(n-1)-5 = A000400(n)+1 = 7*a(n-1) - 6*a(n-2).

G.f.: 1/(1-x)+1/(1-6*x). E.g.f.: e^x+e^(6*x). [Mohammad K. Azarian, Jan 02 2009]

MATHEMATICA

Table[6^n + 1, {n, 0, 20}]

6^Range[0, 20]+1 (* or *) LinearRecurrence[{7, -6}, {2, 7}, 30] (* Harvey P. Dale, Aug 11 2015 *)

PROG

(MAGMA) [6^n + 1: n in [0..30] ]; // Vincenzo Librandi, Apr 30 2011

(PARI) vector(20, n, n--; 6^n + 1) \\ Michel Marcus, Jun 11 2015

CROSSREFS

Cf. A054977, A007395, A000051, A034472, A052539, A034474, A034491, A062395, A062396, A062397, A007689, A063376, A063481, A074600 - A074624, A034524, A178248, A228081 for numbers one more than powers.

Sequence in context: A216362 A047066 A002787 * A245902 A063766 A020040

Adjacent sequences:  A062391 A062392 A062393 * A062395 A062396 A062397

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Jun 22 2001

STATUS

approved

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Last modified June 23 21:29 EDT 2017. Contains 288675 sequences.