A047433 - OEIS

A047433

Numbers that are congruent to {2, 4, 5, 6} mod 8.

2, 4, 5, 6, 10, 12, 13, 14, 18, 20, 21, 22, 26, 28, 29, 30, 34, 36, 37, 38, 42, 44, 45, 46, 50, 52, 53, 54, 58, 60, 61, 62, 66, 68, 69, 70, 74, 76, 77, 78, 82, 84, 85, 86, 90, 92, 93, 94, 98, 100, 101, 102, 106, 108, 109, 110, 114, 116, 117, 118, 122, 124

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

OFFSET

1,1

LINKS

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

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

FORMULA

G.f.: x*(2+2*x+x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

From Wesley Ivan Hurt, May 26 2016: (Start)

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

a(n) = (8*n-3-i^(2*n)-(2-i)*i^(-n)-(2+i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047406(k), a(2k-1) = A047617(k). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (3-sqrt(2))*Pi/16 + log(2)/4 + sqrt(2)*log(sqrt(2)-1)/8. - Amiram Eldar, Dec 25 2021

MAPLE

A047433:=n->(8*n-3-I^(2*n)-(2-I)*I^(-n)-(2+I)*I^n)/4: seq(A047433(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

MATHEMATICA

Select[Range[120], MemberQ[{2, 4, 5, 6}, Mod[#, 8]]&] (* Harvey P. Dale, Mar 04 2011 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [2, 4, 5, 6]]; // Wesley Ivan Hurt, May 26 2016

CROSSREFS

Cf. A047406, A047617.

Sequence in context: A257085 A334736 A265349 * A287332 A029465 A014871

Adjacent sequences: A047430 A047431 A047432 * A047434 A047435 A047436

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved