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A047207 Numbers that are congruent to {0, 1, 3, 4} mod 5. 13
0, 1, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..68.

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

FORMULA

a(n) = floor((5n-3)/4). - Gary Detlefs, Mar 06 2010

G.f.: x^2*(1+2*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=3, b(k)=5*2^(k-2) for k>1. - Philippe Deléham, Oct 17 2011

From Wesley Ivan Hurt, May 30 2016: (Start)

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

a(n) = (10*n-9-i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047209(k), a(2k-1) = A047218(k). (End)

E.g.f.: (4 - sin(x) + cos(x) + (5*x - 4)*sinh(x) + 5*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 30 2016

MAPLE

seq(floor((5*n-3)/4), n=1..57); # Gary Detlefs, Mar 06 2010

MATHEMATICA

Flatten[Table[5*n + {0, 1, 3, 4}, {n, 0, 20}]] (* T. D. Noe, Nov 12 2013 *)

PROG

(PARI) forstep(n=0, 99, [1, 2, 1, 1], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

(MAGMA) [n : n in [0..100] | n mod 5 in [0, 1, 3, 4]]; // Wesley Ivan Hurt, May 30 2016

CROSSREFS

Cf. A030308, A047209, A047218.

Sequence in context: A103202 A188040 A099352 * A266728 A039132 A187970

Adjacent sequences:  A047204 A047205 A047206 * A047208 A047209 A047210

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.