A047454 Numbers that are congruent to {1, 2, 3, 4} mod 8.

1, 2, 3, 4, 9, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35, 36, 41, 42, 43, 44, 49, 50, 51, 52, 57, 58, 59, 60, 65, 66, 67, 68, 73, 74, 75, 76, 81, 82, 83, 84, 89, 90, 91, 92, 97, 98, 99, 100, 105, 106, 107, 108, 113, 114, 115, 116, 121, 122, 123

Offset

1,2

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) = (-5-(-1)^n-(1-i)*(-i)^n-(1+i)*i^n+4*n)/2 where i=sqrt(-1).

G.f.: x*(1+x+x^2+x^3+4*x^4)/((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 15 2012

a(2k) = A047463(k), a(2k-1) = A047471(k). - Wesley Ivan Hurt, Jun 01 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16 + 3*log(2)/8. - Amiram Eldar, Dec 23 2021

Maple

A047454:=n->(-5-I^(2*n)-(1-I)*(-I)^n-(1+I)*I^n+4*n)/2: seq(A047454(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0, 300], MemberQ[{1, 2, 3, 4}, Mod[#, 8]]&] (* Vincenzo Librandi, May 15 2012 *)

Prog

(Magma) I:=[1, 2, 3, 4, 9]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 15 2012
(PARI) my(x='x+O('x^100)); Vec(x*(1+x+x^2+x^3+4*x^4)/((1-x)^2*(1+x)*(1+x^2))) \\ Altug Alkan, Dec 24 2015

Crossrefs

Cf. A047463, A047471.

Sequence in context: A135210 A037468 A265746 * A081870 A165315 A284681

Adjacent sequences: A047451 A047452 A047453 * A047455 A047456 A047457

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved