A047361 Numbers that are congruent to {0, 1, 2, 3} mod 7.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A047352, A047356.

Programs

Magma

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

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

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

Extensions

More terms from Wesley Ivan Hurt, May 23 2016