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A047366 Numbers that are congruent to {1, 3, 4, 5} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 29 08:08 EST 2020. Contains 331337 sequences. (Running on oeis4.)