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A047479 Numbers that are congruent to {0, 1, 5, 7} mod 8. 1
0, 1, 5, 7, 8, 9, 13, 15, 16, 17, 21, 23, 24, 25, 29, 31, 32, 33, 37, 39, 40, 41, 45, 47, 48, 49, 53, 55, 56, 57, 61, 63, 64, 65, 69, 71, 72, 73, 77, 79, 80, 81, 85, 87, 88, 89, 93, 95, 96, 97, 101, 103, 104, 105, 109, 111, 112, 113, 117, 119, 120, 121, 125 (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) = (-7-(-1)^n+(2-i)*(-i)^n+(2+i)*i^n+8*n)/4 where i=sqrt(-1).

G.f.: x^2*(1+4*x+2*x^2+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) = A047522(k), a(2k-1) = A047615(k). - Wesley Ivan Hurt, Jun 01 2016

E.g.f.: (2 - sin(x) + 2*cos(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016

MAPLE

A047479:=n->(-7-I^(2*n)+(2-I)*(-I)^n+(2+I)*I^n+8*n)/4: seq(A047479(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

MATHEMATICA

Select[Range[0, 300], MemberQ[{0, 1, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)

PROG

(MAGMA) I:=[0, 1, 5, 7, 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+4*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

CROSSREFS

Cf. A047522, A047615.

Sequence in context: A080644 A309277 A180241 * A080720 A189034 A112250

Adjacent sequences:  A047476 A047477 A047478 * A047480 A047481 A047482

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 13 22:55 EDT 2021. Contains 345016 sequences. (Running on oeis4.)