A047383 Numbers that are congruent to {1, 5} mod 7.

1, 5, 8, 12, 15, 19, 22, 26, 29, 33, 36, 40, 43, 47, 50, 54, 57, 61, 64, 68, 71, 75, 78, 82, 85, 89, 92, 96, 99, 103, 106, 110, 113, 117, 120, 124, 127, 131, 134, 138, 141, 145, 148, 152, 155, 159, 162, 166, 169

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = ceiling((7*n+2)/2).

a(n) = 7*n - a(n-1) - 8 (with a(1)=1). - Vincenzo Librandi, Aug 05 2010

G.f.: x*(1+4*x+2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

a(1)=1, a(2)=5, a(3)=8; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Dec 24 2012

From Wesley Ivan Hurt, Nov 10 2013: (Start)

a(n) = 4*n - floor((n-1)/2) - 3.

a(2*k-1) = 7*k-6, a(2*k) = 7*k-2. (End)

E.g.f.: 2 + ((14*x - 9)*exp(x) + exp(-x))/4. - David Lovler, Sep 01 2022

Maple

A047383:=n->((-1)^n+14*n-9)/4; seq(A047383(n), n=1..100); # Wesley Ivan Hurt, Nov 10 2013

Mathematica

Flatten[(#+{1, 5})&/@(7Range[0, 25])] (* or *) LinearRecurrence[ {1, 1, -1}, {1, 5, 8}, 80] (* Harvey P. Dale, Dec 24 2012 *)

Prog

(PARI) a(n)=7*n\2-2 \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

Cf. A001106.

Sequence in context: A346308 A214858 A186276 * A322534 A314402 A133795

Adjacent sequences: A047380 A047381 A047382 * A047384 A047385 A047386

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved