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A024219
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a(n) = floor( (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ), where S(n) = {first n+1 positive integers congruent to 1 mod 3}.
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2
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0, 3, 7, 12, 19, 28, 38, 49, 62, 77, 93, 110, 129, 150, 172, 195, 220, 247, 275, 304, 335, 368, 402, 437, 474, 513, 553, 594, 637, 682, 728, 775, 824, 875, 927, 980, 1035, 1092, 1150, 1209, 1270, 1333, 1397, 1462, 1529, 1598, 1668, 1739, 1812, 1887, 1963, 2040
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OFFSET
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1,2
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LINKS
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FORMULA
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Conjecture: a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5);
g.f.: x^2*(-3+2*x-3*x^2+x^3) / ( (x^2+1)*(x-1)^3 ). (End)
The above conjectures are true.
a(n) = floor(n*(9*n^2 + 9*n - 2)/(4*(3*n + 2))).
(End)
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MATHEMATICA
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LinearRecurrence[{3, -4, 4, -3, 1}, {0, 3, 7, 12, 19}, 60] (* Harvey P. Dale, May 20 2019 *)
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PROG
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(PARI) a(n)=floor(sum(j=0, n, sum(k=j+1, n, (3*j+1)*(3*k+1)))/sum(i=0, n, (3*i+1))) \\ Andrew Howroyd, Aug 12 2018
(PARI) a(n) = floor(n*(9*n^2+9*n-2)/(4*(3*n+2))); \\ Andrew Howroyd, Aug 12 2018
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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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EXTENSIONS
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STATUS
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approved
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