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A047430
Numbers that are congruent to {0, 4, 5, 6} mod 8.
1
0, 4, 5, 6, 8, 12, 13, 14, 16, 20, 21, 22, 24, 28, 29, 30, 32, 36, 37, 38, 40, 44, 45, 46, 48, 52, 53, 54, 56, 60, 61, 62, 64, 68, 69, 70, 72, 76, 77, 78, 80, 84, 85, 86, 88, 92, 93, 94, 96, 100, 101, 102, 104, 108, 109, 110, 112, 116, 117, 118, 120, 124
OFFSET
1,2
FORMULA
G.f.: x^2*(4+x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
From Wesley Ivan Hurt, May 25 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-5+i^(2*n)-(2+i)*i^(-n)-(2-i)*i^n)/4 where i=sqrt(-1).
a(2k) = A047406(k), a(2k-1) = A047615(k). (End)
E.g.f.: (4 - sin(x) - 2*cos(x) + (4*x - 3)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016
Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*log(2+sqrt(2))/8 - (2-sqrt(2))*(Pi-log(2))/16. - Amiram Eldar, Dec 23 2021
MAPLE
A047430:=n->(8*n-5+I^(2*n)-(2+I)*I^(-n)-(2-I)*I^n)/4: seq(A047430(n), n=1..100); # Wesley Ivan Hurt, May 25 2016
MATHEMATICA
Table[(8n-5+I^(2n)-(2+I)*I^(-n)-(2-I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 25 2016 *)
Select[Range[0, 124], MemberQ[{0, 4, 5, 6}, Mod[#, 8]] &] (* Michael De Vlieger, May 25 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 4, 5, 6, 8}, 100] (* Harvey P. Dale, Aug 05 2023 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 5, 6]]; // Wesley Ivan Hurt, May 25 2016
CROSSREFS
Sequence in context: A047313 A030343 A030590 * A360448 A204098 A115838
KEYWORD
nonn,easy
STATUS
approved