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A047431 Numbers that are congruent to {1, 4, 5, 6} mod 8. 5
1, 4, 5, 6, 9, 12, 13, 14, 17, 20, 21, 22, 25, 28, 29, 30, 33, 36, 37, 38, 41, 44, 45, 46, 49, 52, 53, 54, 57, 60, 61, 62, 65, 68, 69, 70, 73, 76, 77, 78, 81, 84, 85, 86, 89, 92, 93, 94, 97, 100, 101, 102, 105, 108, 109, 110, 113, 116, 117, 118, 121, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

FORMULA

G.f.: x*(1+2*x-x^2+2*x^3)/((x^2+1)*(x-1)^2). - R. J. Mathar, Oct 08 2011

a(n) = (-2-(-i)^n-i^n+4n)/2 where i=sqrt(-1). - Colin Barker, Jun 06 2012

From Wesley Ivan Hurt, May 30 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

a(2k) = A047406(k), a(2k-1) = A016813(k-1) k>0. (End)

E.g.f.: 2 - cos(x) - (1 - 2*x)*exp(x). - Ilya Gutkovskiy, May 30 2016

MAPLE

A047431:=n->(4*n-2-(-I)^n-I^n)/2: seq(A047431(n), n=1..100); # Wesley Ivan Hurt, May 30 2016

MATHEMATICA

Table[(4n-2-(-I)^n-I^n)/2, {n, 80}] (* Wesley Ivan Hurt, May 30 2016 *)

LinearRecurrence[{2, -2, 2, -1}, {1, 4, 5, 6}, 70] (* Harvey P. Dale, Dec 04 2018 *)

PROG

(Sage) [lucas_number1(n, 0, 1)+2*n+1 for n in xrange(0, 56)] # Zerinvary Lajos, Jul 06 2008

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 4, 5, 6]]; // Wesley Ivan Hurt, May 30 2016

CROSSREFS

Cf. A016813, A047404, A047406, A047546, A056594.

Sequence in context: A010456 A072496 A306482 * A288695 A182719 A003156

Adjacent sequences:  A047428 A047429 A047430 * A047432 A047433 A047434

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 16 13:32 EDT 2019. Contains 328093 sequences. (Running on oeis4.)