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A047365 Numbers that are congruent to {0, 3, 4, 5} mod 7. 1
0, 3, 4, 5, 7, 10, 11, 12, 14, 17, 18, 19, 21, 24, 25, 26, 28, 31, 32, 33, 35, 38, 39, 40, 42, 45, 46, 47, 49, 52, 53, 54, 56, 59, 60, 61, 63, 66, 67, 68, 70, 73, 74, 75, 77, 80, 81, 82, 84, 87, 88, 89, 91, 94, 95, 96, 98, 101, 102, 103, 105, 108, 109, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..64.

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

FORMULA

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

a(1)=0, a(2)=3, a(3)=4, a(4)=5, a(5)=7, a(n)=a(n-1)+a(n-4)-a(n-5) for n>5. - Harvey P. Dale, May 26 2012

From Wesley Ivan Hurt, Jun 04 2016: (Start)

a(n) = (14*n-11+i^(2*n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047389(k), a(2k-1) = A047345(k).

MAPLE

A047365:=n->(14*n-11+I^(2*n)-(3+I)*I^(-n)-(3-I)*I^n)/8: seq(A047365(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 3, 4, 5}, Mod[#, 7]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 4, 5, 7}, 60] (* Harvey P. Dale, May 26 2012 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 04 2016

CROSSREFS

Cf. A047345, A047389.

Sequence in context: A165713 A105148 A072556 * A048342 A159560 A288427

Adjacent sequences:  A047362 A047363 A047364 * A047366 A047367 A047368

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 29 06:21 EDT 2021. Contains 346340 sequences. (Running on oeis4.)