A047403 - OEIS

A047403

Numbers that are congruent to {0, 2, 3, 6} mod 8.

0, 2, 3, 6, 8, 10, 11, 14, 16, 18, 19, 22, 24, 26, 27, 30, 32, 34, 35, 38, 40, 42, 43, 46, 48, 50, 51, 54, 56, 58, 59, 62, 64, 66, 67, 70, 72, 74, 75, 78, 80, 82, 83, 86, 88, 90, 91, 94, 96, 98, 99, 102, 104, 106, 107, 110, 112, 114, 115, 118, 120, 122, 123, 126, 128

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..65.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

a(n) = 2*n - ((n mod 4) == 2).

G.f.: x^2*(2+x+3*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, May 24 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (8*n-9+i^(2*n)+i^(1-n)-i^(1+n))/4, where i=sqrt(-1).

a(2k) = A016825(k-1) for k>0, a(2k-1) = A047470. (End)

E.g.f.: (4 + sin(x) + (4*x - 5)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016

Sum_{n>=2} (-1)^n/a(n) = (4-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - (sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 21 2021

MAPLE

A047403:=n->(8*n-9+I^(2*n)+I^(1-n)-I^(1+n))/4: seq(A047403(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

MATHEMATICA

Table[(8n-9+I^(2n)+I^(1-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)

#+{0, 2, 3, 6}&/@(8*Range[0, 20])//Flatten (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 3, 6, 8}, 80] (* Harvey P. Dale, Mar 02 2023 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 6]]; // Wesley Ivan Hurt, May 24 2016

CROSSREFS

Cf. A016825, A047470.

Sequence in context: A351125 A334747 A285306 * A286051 A093193 A187750

Adjacent sequences: A047400 A047401 A047402 * A047404 A047405 A047406

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved