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 A047377 Numbers that are congruent to {0, 1, 4, 5} mod 7. 1
 0, 1, 4, 5, 7, 8, 11, 12, 14, 15, 18, 19, 21, 22, 25, 26, 28, 29, 32, 33, 35, 36, 39, 40, 42, 43, 46, 47, 49, 50, 53, 54, 56, 57, 60, 61, 63, 64, 67, 68, 70, 71, 74, 75, 77, 78, 81, 82, 84, 85, 88, 89, 91, 92, 95, 96, 98, 99, 102, 103, 105, 106, 109, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS 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)=4 and b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 25 2011 G.f.: x^2*(1+3*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 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) = (14*n-15-3*i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n)/8, where i=sqrt(-1). a(2k) = A047383(k), a(2k-1) = A047345(k). (End) E.g.f.: (8 - sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 9)*cosh(x))/4. - Ilya Gutkovskiy, May 25 2016 MAPLE A047377:=n->(14*n-15-3*I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/8: seq(A047377(n), n=1..100); # Wesley Ivan Hurt, May 24 2016 MATHEMATICA Table[(14n-15-3*I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *) Select[Range@ 120, MemberQ[{0, 1, 4, 5}, Mod[#, 7]] &] (* Michael De Vlieger, May 24 2016 *) PROG (MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 4, 5]]; // Wesley Ivan Hurt, May 24 2016 CROSSREFS Cf. A030308, A047345, A047383. Sequence in context: A159698 A191276 A228919 * A188265 A032714 A032702 Adjacent sequences:  A047374 A047375 A047376 * A047378 A047379 A047380 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, May 24 2016 STATUS approved

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