A047439 Numbers that are congruent to {0, 1, 5, 6} mod 8.

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

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)

Sum_{n>=2} (-1)^n/a(n) = (2*sqrt(2)-1)*Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - Amiram Eldar, Dec 20 2021

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: A347872 A191355 A337143 * A095763 A342781 A187843

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