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A047468 Numbers that are congruent to {1, 2} mod 8. 1
1, 2, 9, 10, 17, 18, 25, 26, 33, 34, 41, 42, 49, 50, 57, 58, 65, 66, 73, 74, 81, 82, 89, 90, 97, 98, 105, 106, 113, 114, 121, 122, 129, 130, 137, 138, 145, 146, 153, 154, 161, 162, 169, 170, 177, 178, 185, 186, 193, 194, 201, 202, 209, 210, 217, 218, 225, 226, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..59.

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

FORMULA

a(n) = 8*n - a(n-1) - 13 (with a(1)=1). - Vincenzo Librandi, Aug 06 2010

G.f.: x*(1+x+6*x^2)/((1-x)^2*(1+x)). - Colin Barker, May 13 2012

a(n) = 1 + 8*floor((n-1)/2) + ((n-1) mod 2). - Alois P. Heinz, May 13 2012

a(n) = (-3*(3 + (-1)^n) + 8*n)/2. - Colin Barker, May 14 2012

a(1)=1, a(2)=2, a(3)=9, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Mar 26 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021

MATHEMATICA

Flatten[#+{1, 2}&/@(8Range[0, 30])] (* or *) LinearRecurrence[{1, 1, -1}, {1, 2, 9}, 60] (* Harvey P. Dale, Mar 26 2013 *)

PROG

(PARI) a(n)=(n-1)\2*8+2-n%2 \\ Charles R Greathouse IV, May 14 2012

CROSSREFS

Union of A017077 and A017089.

Cf. A047467.

Sequence in context: A078180 A058890 A306998 * A032929 A226832 A320919

Adjacent sequences:  A047465 A047466 A047467 * A047469 A047470 A047471

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vincenzo Librandi, Aug 06 2010

STATUS

approved

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Last modified May 21 07:22 EDT 2022. Contains 353889 sequences. (Running on oeis4.)