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A295130
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a(n) = 3*n*(64*n^2 + 1).
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2
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195, 1542, 5193, 12300, 24015, 41490, 65877, 98328, 139995, 192030, 255585, 331812, 421863, 526890, 648045, 786480, 943347, 1119798, 1316985, 1536060, 1778175, 2044482, 2336133, 2654280, 3000075, 3374670, 3779217, 4214868, 4682775, 5184090, 5719965, 6291552, 6900003, 7546470, 8232105, 8958060, 9725487
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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Martin Gardner, Mathematical Carnival, 1975, Alfred A. Knopf Inc., New York.
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LINKS
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FORMULA
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a(n) = 3*n*(64*n^2 + 1).
G.f.: 3*x*(65 + 254*x + 65*x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
E.g.f.: 3*x*e^x * (65 + 192*x + 64*x^2). - Iain Fox, Dec 22 2017
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EXAMPLE
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For examples see "Squares in a square" in the LINKS section.
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MATHEMATICA
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f[n_] := 3n (64n^2 +1); Array[f, 33] (* or *)
CoefficientList[ Series[(3 (65 +254x +65x^2))/(-1 +x)^4, {x, 0, 33}], x] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {195, 1542, 5193, 12300}, 34] (* Robert G. Wilson v, Dec 27 2017 *)
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PROG
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(PARI) Vec(3*x*(65 + 254*x + 65*x^2) / (1 - x)^4 + O(x^40)) \\ Colin Barker, Nov 23 2017
(PARI) a(n) = 192*n^3 + 3*n \\ Iain Fox, Dec 22 2017
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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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