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URL: https://oeis.org/A047401

⇱ A047401 - OEIS

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A047401
Numbers that are congruent to {0, 1, 3, 6} mod 8.
2
0, 1, 3, 6, 8, 9, 11, 14, 16, 17, 19, 22, 24, 25, 27, 30, 32, 33, 35, 38, 40, 41, 43, 46, 48, 49, 51, 54, 56, 57, 59, 62, 64, 65, 67, 70, 72, 73, 75, 78, 80, 81, 83, 86, 88, 89, 91, 94, 96, 97, 99, 102, 104, 105, 107, 110, 112, 113, 115, 118, 120, 121, 123
OFFSET
1,3
COMMENTS
Partial sums of A068073. - Jeremy Gardiner, Jul 20 2013.
FORMULA
G.f.: x^2*(1+x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011
a(n) = 2*(n-1)+(i^(n*(n-1))-1)/2, where i=sqrt(-1). - Bruno Berselli, Dec 05 2011
From Wesley Ivan Hurt, Jun 01 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(2k) = A047452(k), a(2k-1) = A047470(k). (End)
Sum_{n>=2} (-1)^n/a(n) = Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - Amiram Eldar, Dec 20 2021
MAPLE
A047401:=n->2*(n-1)+(I^(n*(n-1))-1)/2: seq(A047401(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016
MATHEMATICA
Select[Range[0, 107], MemberQ[{0, 1, 3, 6}, Mod[#, 8]]&] (* Bruno Berselli, Dec 05 2011 *)
PROG
(Maxima) makelist(2*(n-1)+(%i^(n*(n-1))-1)/2, n, 1, 55); /* Bruno Berselli, Dec 05 2011 */
(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 6]]; // Wesley Ivan Hurt, Jun 01 2016
(PARI) my(x='x+O('x^100)); concat(0, Vec(x^2*(1+x+2*x^2)/((x^2+1)*(x-1)^2))) \\ Altug Alkan, Jun 02 2016
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved