A047371 Numbers that are congruent to {0, 2, 3, 5} mod 7.

0, 2, 3, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 24, 26, 28, 30, 31, 33, 35, 37, 38, 40, 42, 44, 45, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 86, 87, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 107, 108, 110

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

a(n) = floor((7n-6)/4). [Gary Detlefs, Mar 06 2010]

G.f.: x^2*(2+x+2*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 04 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = i^(-n)*((14*n-15)*i^n+i-1-(1+i)*i^(2*n)+i^(-n))/8 where i=sqrt(-1).

a(2k) = A047385(k), a(2k-1) = A047355(k). (End)

E.g.f.: (8 + sin(x) - cos(x) + (7*x - 8)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016

Maple

seq(floor((7*n-6)/4), n=1..56); # [Gary Detlefs, Mar 06 2010]

Mathematica

Table[I^(-n)*((14n-15)*I^n+I-1-(1+I)*I^(2n)+I^(-n))/8, {n, 80}] (* Wesley Ivan Hurt, Jun 04 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 3, 5, 7}, 70] (* Harvey P. Dale, Oct 24 2018 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 2, 3, 5]]; // Wesley Ivan Hurt, Jun 04 2016

Crossrefs

Cf. A047355, A047385.

Sequence in context: A081477 A083033 A022847 * A327492 A044918 A103635

Adjacent sequences: A047368 A047369 A047370 * A047372 A047373 A047374

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved