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A316466
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a(n) = 2*n*(7*n - 3).
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10
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0, 8, 44, 108, 200, 320, 468, 644, 848, 1080, 1340, 1628, 1944, 2288, 2660, 3060, 3488, 3944, 4428, 4940, 5480, 6048, 6644, 7268, 7920, 8600, 9308, 10044, 10808, 11600, 12420, 13268, 14144, 15048, 15980, 16940, 17928, 18944, 19988, 21060, 22160, 23288, 24444, 25628, 26840
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OFFSET
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0,2
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COMMENTS
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This is the case k = 9 of Sum_{i = 2..k} P(i,n) = (k - 1)*n*((k - 2)*n - (k - 6))/4, where P(k,n) = n*((k - 2)*n - (k - 4))/2 (see Crossrefs for similar sequences and "Square array in A139600" in Links section).
14*x + 9 is a square for x = a(n) or x = a(-n).
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LINKS
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FORMULA
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O.g.f.: 4*x*(2 + 5*x)/(1 - x)^3.
E.g.f.: 2*x*(4 + 7*x)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
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MATHEMATICA
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Table[2 n (7 n - 3), {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {0, 8, 44}, 50] (* Harvey P. Dale, Jan 24 2021 *)
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PROG
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(PARI) vector(50, n, n--; 2*n*(7*n-3))
(PARI) concat(0, Vec(4*x*(2 + 5*x)/(1 - x)^3 + O(x^40))) \\ Colin Barker, Jul 05 2018
(Sage) [2*n*(7*n-3) for n in (0..50)]
(Maxima) makelist(2*n*(7*n-3), n, 0, 50);
(GAP) List([0..50], n -> 2*n*(7*n-3));
(Magma) [2*n*(7*n-3): n in [0..50]];
(Python) [2*n*(7*n-3) for n in range(50)]
(Julia) [2*n*(7*n-3) for n in 0:50] |> println
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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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