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A047372
Numbers that are congruent to {1, 2, 3, 5} mod 7.
1
1, 2, 3, 5, 8, 9, 10, 12, 15, 16, 17, 19, 22, 23, 24, 26, 29, 30, 31, 33, 36, 37, 38, 40, 43, 44, 45, 47, 50, 51, 52, 54, 57, 58, 59, 61, 64, 65, 66, 68, 71, 72, 73, 75, 78, 79, 80, 82, 85, 86, 87, 89, 92, 93, 94, 96, 99, 100, 101, 103, 106, 107, 108, 110
OFFSET
1,2
FORMULA
From Bruno Berselli, Dec 01 2010: (Start)
G.f.: x*(1+x+x^2+2*x^3+2*x^4) / ((1-x)^2*(1+x+x^2+x^3)).
a(n) = (14*n+(3*i-1)*(-i)^n-(3*i+1)*i^n-(-1)^n-13)/8, i=sqrt(-1). (End)
From Wesley Ivan Hurt, Jun 04 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(2k) = A047385(k), a(2k-1) = A047356(k). (End)
E.g.f.: (8 + 3*sin(x) - cos(x) + (7*x - 6)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016
MAPLE
A047372:=n->(14*n+(3*I-1)*(-I)^n-(3*I+1)*I^n-(-1)^n-13)/8: seq(A047372(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016
MATHEMATICA
Flatten[7Range[0, 12]+n/.n->{1, 2, 3, 5}] (* Harvey P. Dale, Dec. 13, 2010 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [1, 2, 3, 5]]; // Wesley Ivan Hurt, Jun 04 2016
CROSSREFS
Sequence in context: A002153 A047607 A113051 * A308469 A247547 A096974
KEYWORD
nonn,easy
STATUS
approved