A072682 Numbers congruent to {3, 36, 54, 57} mod 60.
3, 36, 54, 57, 63, 96, 114, 117, 123, 156, 174, 177, 183, 216, 234, 237, 243, 276, 294, 297, 303, 336, 354, 357, 363, 396, 414, 417, 423, 456, 474, 477, 483, 516, 534, 537, 543, 576, 594, 597, 603, 636, 654, 657, 663, 696, 714, 717, 723, 756, 774, 777, 783
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Magma
[n: n in [0..800] | n mod 60 in [3, 36, 54, 57]]; // Bruno Berselli, Jun 14 2016
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Maple
A072682:=n->15*n+3*(1+I)*((1-I)*I^(2*n)-(5+2*I)*I^(-n)+(2+5*I)*I^n)/4: seq(A072682(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
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Mathematica
Select[Range[800], MemberQ[{3,36,54,57}, Mod[#,60]]&] (* Harvey P. Dale, Apr 07 2013 *)
Formula
Sequence contains numbers of the form: 3+60k, 36+60k, 54+60k, 57+60k, k>=0.
G.f.: 3*x*(1 + 11*x + 6*x^2 + x^3 + x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = 15*n + 3*(1+i)*((1-i)*i^(2*n) - (5+2*i)*i^(-n) + (2+5*i)*i^n)/4 where i=sqrt(-1). (End)
Extensions
Simpler definition from Ralf Stephan, Jun 18 2005
Comments