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A047439 Numbers that are congruent to {0, 1, 5, 6} mod 8. 1
0, 1, 5, 6, 8, 9, 13, 14, 16, 17, 21, 22, 24, 25, 29, 30, 32, 33, 37, 38, 40, 41, 45, 46, 48, 49, 53, 54, 56, 57, 61, 62, 64, 65, 69, 70, 72, 73, 77, 78, 80, 81, 85, 86, 88, 89, 93, 94, 96, 97, 101, 102, 104, 105, 109, 110, 112, 113, 117, 118, 120, 121, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..63.

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

FORMULA

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=5 and b(k)=2^(k+1) for k>1. - Philippe Deléham, Oct 19 2011

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

a(n) = Sum_{i=1..n} gcd(i+2, i-2). - Wesley Ivan Hurt, Jan 23 2014

From Wesley Ivan Hurt, May 22 2016: (Start)

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

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

a(2n) = A047452, a(2n-1) = A047615(n). (End)

MAPLE

A047439:=n->add(gcd(i+2, i-2), i=1..n); seq(A047439(n), n=0..100); # Wesley Ivan Hurt, Jan 23 2014

MATHEMATICA

Table[Sum[GCD[i + 2, i - 2], {i, n}], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 23 2014 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [0, 1, 5, 6]]; // Wesley Ivan Hurt, May 22 2016

CROSSREFS

Cf. A030308, A047452, A047615.

Sequence in context: A120174 A184817 A191355 * A095763 A187843 A155146

Adjacent sequences:  A047436 A047437 A047438 * A047440 A047441 A047442

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 22 2016

STATUS

approved

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Last modified April 24 00:02 EDT 2019. Contains 322404 sequences. (Running on oeis4.)