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A274757
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Numbers k such that 6*k+1 is a triangular number (A000217).
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4
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0, 9, 15, 42, 54, 99, 117, 180, 204, 285, 315, 414, 450, 567, 609, 744, 792, 945, 999, 1170, 1230, 1419, 1485, 1692, 1764, 1989, 2067, 2310, 2394, 2655, 2745, 3024, 3120, 3417, 3519, 3834, 3942, 4275, 4389, 4740, 4860, 5229, 5355, 5742, 5874, 6279, 6417
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OFFSET
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1,2
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COMMENTS
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Numbers of the type floor(3*m*(m+1)/4) for which floor(3*m*(m+1)/4) = 3*floor(m*(m+1)/4). A014601 lists the values of m. - Bruno Berselli, Jan 13 2017
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LINKS
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FORMULA
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G.f.: 3*x^2*(3 + 2*x + 3*x^2) / ((1 - x)^3*(1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5.
a(n) = 3*(2*n - 1)*(2*n + (-1)^n - 1)/4. Therefore:
a(n) = 3*n*(2*n - 1)/2 for n even,
a(n) = 3*(n-1)*(2*n - 1)/2 for n odd.
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MATHEMATICA
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Table[3 (2 n - 1) (2 n + (-1)^n - 1)/4, {n, 1, 60}] (* Bruno Berselli, Jul 08 2016 *)
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PROG
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(PARI) isok(n) = ispolygonal(6*n+1, 3)
(PARI) select(n->ispolygonal(6*n+1, 3), vector(7000, n, n-1))
(PARI) concat(0, Vec(3*x^2*(3+2*x+3*x^2)/((1-x)^3*(1+x)^2) + O(x^60)))
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CROSSREFS
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Cf. similar sequences listed in A274830.
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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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