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 A047553 Numbers that are congruent to {0, 2, 6, 7} mod 8. 1
 0, 2, 6, 7, 8, 10, 14, 15, 16, 18, 22, 23, 24, 26, 30, 31, 32, 34, 38, 39, 40, 42, 46, 47, 48, 50, 54, 55, 56, 58, 62, 63, 64, 66, 70, 71, 72, 74, 78, 79, 80, 82, 86, 87, 88, 90, 94, 95, 96, 98, 102, 103, 104, 106, 110, 111, 112, 114, 118, 119, 120, 122, 126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From Wesley Ivan Hurt, May 29 2016: (Start) G.f.: x^2*(2+4*x+x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)). a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(n) = (8*n-5-i^(2*n)+(1-2*i)*i^(-n)+(1+2*i)*i^n)/4 where i=sqrt(-1). a(2k) = A047524(k), a(2k-1) = A047451(k). (End) E.g.f.: (2 - 2*sin(x) + cos(x) + (4*x - 2)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 29 2016 MAPLE A047553:=n->(8*n-5-I^(2*n)+(1-2*I)*I^(-n)+(1+2*I)*I^n)/4: seq(A047553(n), n=1..100); # Wesley Ivan Hurt, May 29 2016 MATHEMATICA Select[Range[0, 200], MemberQ[{0, 2, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Aug 09 2013 *) PROG (MAGMA) [n : n in [0..150] | n mod 8 in [0, 2, 6, 7]]; // Wesley Ivan Hurt, May 29 2016 CROSSREFS Cf. A047451, A047524. Sequence in context: A028735 A267541 A325465 * A139418 A190212 A327179 Adjacent sequences:  A047550 A047551 A047552 * A047554 A047555 A047556 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 16 03:37 EDT 2021. Contains 343030 sequences. (Running on oeis4.)