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A047460 Numbers that are congruent to {0, 1, 3, 4} mod 8. 1
0, 1, 3, 4, 8, 9, 11, 12, 16, 17, 19, 20, 24, 25, 27, 28, 32, 33, 35, 36, 40, 41, 43, 44, 48, 49, 51, 52, 56, 57, 59, 60, 64, 65, 67, 68, 72, 73, 75, 76, 80, 81, 83, 84, 88, 89, 91, 92, 96, 97, 99, 100, 104, 105, 107, 108, 112, 113, 115, 116, 120, 121, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

From Colin Barker, May 14 2012: (Start)

a(n) = (-1/4+i/4)*((6+6*i)+(1+i)*(-1)^n+(-i)^n+i*i^n)+2*n where i=sqrt(-1).

G.f.: x^2*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 16 2012

a(2k) = A047461(k), a(2k-1) = A047470(k). - Wesley Ivan Hurt, Jun 01 2016

MAPLE

A047460:=n->(-1/4+I/4)*((6+6*I)+(1+I)*I^(2*n)+(-I)^n+I*I^n)+2*n: seq(A047460(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

MATHEMATICA

Select[Range[0, 3000], MemberQ[{0, 1, 3, 4}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)

PROG

(MAGMA) I:=[0, 1, 3, 4, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012

(PARI) x='x+O('x^100); concat(0, Vec(x^2*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

CROSSREFS

Cf. A047461, A047470.

Sequence in context: A243064 A057549 A284392 * A193532 A068056 A006520

Adjacent sequences:  A047457 A047458 A047459 * A047461 A047462 A047463

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 25 07:47 EST 2020. Contains 331241 sequences. (Running on oeis4.)