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A047371 Numbers that are congruent to {0, 2, 3, 5} mod 7. 1
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 (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

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

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Last modified February 19 10:03 EST 2020. Contains 332041 sequences. (Running on oeis4.)