A258340 a(n) = (7^n + 3^n - 2)/8.

1, 7, 46, 310, 2131, 14797, 103216, 721420, 5046661, 35316787, 247187986, 1730227330, 12111325591, 84778481977, 593446982356, 4154121702040, 29078830390921, 203551748166367, 1424862043454326, 9974033723049550, 69818234317954651, 488727634995505957

Offset

1,2

Comments

This sequence appeared on an test given to job interviewers.

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Formula

a(n) = (A074608(n) - 2)/8. - Michel Marcus, Aug 20 2015

G.f.: x*(1-4*x)/((1-x)*(1-3*x)*(1-7*x)). - Vincenzo Librandi, Aug 22 2015

a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) with n>2, a(0)=0. - Bruno Berselli, Aug 24 2015

a(n) = Sum_{k=1..n} A027907(n,2k)*4^(k-1) . - J. Conrad, Aug 30 2016

Mathematica

Table[(7^n + 3^n - 2)/8, {n, 1, 30}] (* Bruno Berselli, Aug 24 2015 *)
LinearRecurrence[{11, -31, 21}, {1, 7, 46}, 30] (* Harvey P. Dale, May 01 2018 *)

Prog

(PARI) first(m)=vector(m, i, (3^i+7^i-2)/8) \\ Anders Hellström, Aug 20 2015
(Magma) [(3^n+7^n-2)/8: n in [1..30]]; // Vincenzo Librandi, Aug 22 2015
(Sage) [(7^n+3^n-2)/8 for n in (1..30)] # Bruno Berselli, Aug 24 2015

Crossrefs

Cf. A074608.

Sequence in context: A128597 A190972 A254601 * A244265 A240722 A365773

Adjacent sequences: A258337 A258338 A258339 * A258341 A258342 A258343

Keyword

nonn,easy

Author

Edwin McCravy, Aug 05 2015

Status

approved