

A047493


Numbers that are congruent to {1, 4, 5, 7} mod 8.


1



1, 4, 5, 7, 9, 12, 13, 15, 17, 20, 21, 23, 25, 28, 29, 31, 33, 36, 37, 39, 41, 44, 45, 47, 49, 52, 53, 55, 57, 60, 61, 63, 65, 68, 69, 71, 73, 76, 77, 79, 81, 84, 85, 87, 89, 92, 93, 95, 97, 100, 101, 103, 105, 108, 109, 111, 113, 116, 117, 119, 121, 124
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..62.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,1).


FORMULA

G.f.: x*(1+3*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x1)^2 ).  R. J. Mathar, Nov 06 2015
From Wesley Ivan Hurt, May 26 2016: (Start)
a(n) = a(n1) + a(n4)  a(n5) for n>5.
a(n) = (8*n3+i^(2*n)i^(n)i^n)/4 where i=sqrt(1).
a(2k) = A047535(k), a(2k1) = A016813(k1) for n>0. (End)
E.g.f.: (2  cos(x) + (4*x  2)*sinh(x) + (4*x  1)*cosh(x))/2.  Ilya Gutkovskiy, May 27 2016


MAPLE

A047493:=n>(8*n3+I^(2*n)I^(n)I^n)/4: seq(A047493(n), n=1..100); # Wesley Ivan Hurt, May 26 2016


MATHEMATICA

Table[(8n3+I^(2n)I^(n)I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
LinearRecurrence[{1, 0, 0, 1, 1}, {1, 4, 5, 7, 9}, 80] (* Harvey P. Dale, May 05 2018 *)


PROG

(MAGMA) [n : n in [0..150]  n mod 8 in [1, 4, 5, 7]]; // Wesley Ivan Hurt, May 26 2016


CROSSREFS

Cf. A016813, A047535.
Sequence in context: A035255 A335984 A286050 * A285307 A297838 A032360
Adjacent sequences: A047490 A047491 A047492 * A047494 A047495 A047496


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



