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1, 2, 3, 5, 7, 6, 9, 12, 9, 13, 17, 12, 17, 22, 15, 21, 27, 18, 25, 32, 21, 29, 37, 24, 33, 42, 27, 37, 47, 30, 41, 52, 33, 45, 57, 36, 49, 62, 39, 53, 67, 42, 57, 72, 45, 61, 77, 48, 65, 82, 51, 69, 87, 54, 73, 92, 57, 77, 97, 60, 81, 102, 63, 85, 107, 66, 89, 112, 69, 93, 117
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OFFSET
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1,2
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COMMENTS
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Three arithmetic progressions interlaced: a(1..3) = 1..3 and d = a(n+3)-a(n) = 4,5,3.
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LINKS
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FORMULA
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a(n) = n+floor(n/3)*(n mod 3), n = 1, 2, ...
G.f.: x*(3*x^4+3*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, May 11 2015
E.g.f.: (-5+12*x)*exp(x)/9 + (3+2*x)*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2)/9 + 5*exp(-x/2)*cos(sqrt(3)*x/2)/9. - Robert Israel, May 11 2015
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MAPLE
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seq(op([1+4*j, 2+5*j, 3+3*j]), j=0..100); # Robert Israel, May 11 2015
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MATHEMATICA
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Table[n+Floor[n/3]*Mod[n, 3], {n, 78}]
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 2, 3, 5, 7, 6}, 80] (* Harvey P. Dale, Aug 06 2021 *)
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PROG
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(PARI) Vec(x*(3*x^4+3*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, May 11 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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