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A047403
Numbers that are congruent to {0, 2, 3, 6} mod 8.
1
0, 2, 3, 6, 8, 10, 11, 14, 16, 18, 19, 22, 24, 26, 27, 30, 32, 34, 35, 38, 40, 42, 43, 46, 48, 50, 51, 54, 56, 58, 59, 62, 64, 66, 67, 70, 72, 74, 75, 78, 80, 82, 83, 86, 88, 90, 91, 94, 96, 98, 99, 102, 104, 106, 107, 110, 112, 114, 115, 118, 120, 122, 123, 126, 128
OFFSET
1,2
FORMULA
a(n) = 2*n - ((n mod 4) == 2).
G.f.: x^2*(2+x+3*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011
From Wesley Ivan Hurt, May 24 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-9+i^(2*n)+i^(1-n)-i^(1+n))/4, where i=sqrt(-1).
a(2k) = A016825(k-1) for k>0, a(2k-1) = A047470. (End)
E.g.f.: (4 + sin(x) + (4*x - 5)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016
Sum_{n>=2} (-1)^n/a(n) = (4-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - (sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 21 2021
MAPLE
A047403:=n->(8*n-9+I^(2*n)+I^(1-n)-I^(1+n))/4: seq(A047403(n), n=1..100); # Wesley Ivan Hurt, May 24 2016
MATHEMATICA
Table[(8n-9+I^(2n)+I^(1-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)
#+{0, 2, 3, 6}&/@(8*Range[0, 20])//Flatten (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 3, 6, 8}, 80] (* Harvey P. Dale, Mar 02 2023 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 6]]; // Wesley Ivan Hurt, May 24 2016
CROSSREFS
Sequence in context: A351125 A334747 A285306 * A286051 A093193 A187750
KEYWORD
nonn,easy
STATUS
approved