A047466 - OEIS

A047466

Numbers that are congruent to {0, 1, 2, 4} mod 8.

0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 24, 25, 26, 28, 32, 33, 34, 36, 40, 41, 42, 44, 48, 49, 50, 52, 56, 57, 58, 60, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 88, 89, 90, 92, 96, 97, 98, 100, 104, 105, 106, 108, 112, 113, 114, 116, 120, 121, 122

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x^2*(1+x+2*x^2+4*x^3) / ( (1+x)*(1+x^2)*(1-x)^2 ). - R. J. Mathar, Oct 08 2011

a(n) = 2*n-4+(3-(-1)^n)*(1-i^(n*(n+1)))/4, where i=sqrt(-1). - Bruno Berselli, Jul 18 2012

From Wesley Ivan Hurt, Jun 01 2016: (Start)

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

a(2k) = A047461(k), a(2k-1) = A047467(k). (End)

Sum_{n>=2} (-1)^n/a(n) = (1+2*sqrt(2))*Pi/32 + (3+sqrt(2))*log(2)/16 - sqrt(2)*log(2-sqrt(2))/8. - Amiram Eldar, Dec 20 2021

MAPLE

A047466:=n->2*n-4+(3-I^(2*n))*(1-I^(n*(n+1)))/4: seq(A047466(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

MATHEMATICA

Select[Range[0, 120], MemberQ[{0, 1, 2, 4}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 4, 8}, 60] (* Bruno Berselli, Jul 18 2012 *)

PROG

Contribution from Bruno Berselli, Jul 18 2012: (Start)

(Magma) [n: n in [0..120] | n mod 8 in [0, 1, 2, 4]];

(Maxima) makelist(2*n-4+(3-(-1)^n)*(1-%i^(n*(n+1)))/4, n, 1, 60);

(PARI) concat(0, Vec((1+x+2*x^2+4*x^3)/((1+x)*(1+x^2)*(1-x)^2)+O(x^60))) (End)

CROSSREFS

Essentially the same as A003485.

Cf. A047461, A047467.

Sequence in context: A196000 A044952 A352831 * A003485 A072602 A374664

Adjacent sequences: A047463 A047464 A047465 * A047467 A047468 A047469

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved