A047366 - OEIS

A047366

Numbers that are congruent to {1, 3, 4, 5} mod 7.

1, 3, 4, 5, 8, 10, 11, 12, 15, 17, 18, 19, 22, 24, 25, 26, 29, 31, 32, 33, 36, 38, 39, 40, 43, 45, 46, 47, 50, 52, 53, 54, 57, 59, 60, 61, 64, 66, 67, 68, 71, 73, 74, 75, 78, 80, 81, 82, 85, 87, 88, 89, 92, 94, 95, 96, 99, 101, 102, 103, 106, 108, 109, 110

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..64.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

G.f.: x*(1+2*x+x^2+x^3+2*x^4) / ( (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) = (14n-9-i^(2n)-(3-i)*i^(-n)-(3+i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047389(k), a(2k-1) = A047346(k). (End)

E.g.f.: (8 + sin(x) - 3*cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, May 25 2016

MAPLE

A047366:=n->(14*n-9-I^(2*n)-(3-I)*I^(-n)-(3+I)*I^n)/8: seq(A047366(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

MATHEMATICA

Table[(14n-9-I^(2n)-(3-I)*I^(-n)-(3+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)

Select[Range@ 120, MemberQ[{1, 3, 4, 5}, Mod[#, 7]] &] (* Michael De Vlieger, May 24 2016 *)

PROG

(Magma) [n : n in [0..150] | n mod 7 in [1, 3, 4, 5]]; // Wesley Ivan Hurt, May 24 2016

CROSSREFS

Cf. A047346, A047389.

Sequence in context: A001602 A308197 A087012 * A184776 A202104 A190246

Adjacent sequences: A047363 A047364 A047365 * A047367 A047368 A047369

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 24 2016

STATUS

approved