A047460 Numbers that are congruent to {0, 1, 3, 4} mod 8.

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

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

Sum_{n>=2} (-1)^n/a(n) = Pi/8 + (2-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - Amiram Eldar, Dec 20 2021

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) my(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