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A047361 Numbers that are congruent to {0, 1, 2, 3} mod 7. 2
0, 1, 2, 3, 7, 8, 9, 10, 14, 15, 16, 17, 21, 22, 23, 24, 28, 29, 30, 31, 35, 36, 37, 38, 42, 43, 44, 45, 49, 50, 51, 52, 56, 57, 58, 59, 63, 64, 65, 66, 70, 71, 72, 73, 77, 78, 79, 80, 84, 85, 86, 87, 91, 92, 93, 94, 98, 99, 100, 101, 105, 106, 107, 108, 112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Nonnegative m for which floor(2*m/7) = 2*floor(m/7). [Bruno Berselli, Dec 03 2015]

LINKS

Table of n, a(n) for n=1..65.

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

FORMULA

a(n) = 7*floor(n/4) + (n mod 4), with offset 0 and a(0) = 0. - Gary Detlefs, Mar 09 2010

G.f.: x^2*(1+x+x^2+4*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, May 23 2016: (Start)

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

a(n) = (14*n-23-3*i^(2*n)-(3-3*i)*i^(-n)-(3+3*i)*i^n)/8, where i=sqrt(-1).

a(2k) = A047356(k), a(2k-1) = A047352(k). (End)

E.g.f.: (16 + 3*(sin(x) - cos(x)) + (7*x - 10)*sinh(x) + (7*x - 13)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

MAPLE

A047361:=n->(14*n-23-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8: seq(A047361(n), n=1..100); # Wesley Ivan Hurt, May 23 2016

MATHEMATICA

Flatten[#+{0, 1, 2, 3}&/@(7*Range[0, 20])] (* Harvey P. Dale, Jan 17 2013 *)

PROG

(PARI) concat(0, Vec(x^2*(1+x+x^2+4*x^3)/((1+x)*(x^2+1)*(x-1)^2) + O(x^100))) \\ Altug Alkan, Dec 09 2015

(MAGMA) [n : n in [0..150] | n mod 7 in [0..3]]; // Wesley Ivan Hurt, May 23 2016

CROSSREFS

Cf. A047352, A047356.

Sequence in context: A118374 A154432 A251391 * A037461 A284514 A268398

Adjacent sequences:  A047358 A047359 A047360 * A047362 A047363 A047364

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 23 2016

STATUS

approved

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Last modified October 1 15:55 EDT 2020. Contains 337443 sequences. (Running on oeis4.)