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A134593
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a(n) = 5*n^2 + 10*n + 1. Coefficients of the rational part of (1 + sqrt(n))^5.
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4
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1, 16, 41, 76, 121, 176, 241, 316, 401, 496, 601, 716, 841, 976, 1121, 1276, 1441, 1616, 1801, 1996, 2201, 2416, 2641, 2876, 3121, 3376, 3641, 3916, 4201, 4496, 4801, 5116, 5441, 5776, 6121, 6476, 6841, 7216, 7601, 7996, 8401, 8816, 9241, 9676, 10121
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OFFSET
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0,2
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COMMENTS
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(1+sqrt(n))^5 = (5*n^2 + 10*n + 1) + (n^2 + 10*n + 5)*sqrt(n). Coefficients of the irrational part are A134594.
Number of entries required to describe the options and constraints in Don Knuth's formulation of the n nonattacking queens on an n X n board problem (A000170) as input for his DLX (Dancing Links eXact coverage) program. Can be seen as "entries successfully read" in the video from his 2018 Annual Christmas Lecture. - Hugo Pfoertner, Jan 09 2019
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LINKS
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FORMULA
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a(n) = 5*n^2 + 10*n + 1.
G.f.: (4*x^2 - 13*x - 1)/(x-1)^3. - R. J. Mathar, Nov 14 2007
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MATHEMATICA
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Table[(5n^2 + 10n + 1), {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {1, 16, 41}, 50] (* Harvey P. Dale, Oct 20 2023 *)
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PROG
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(Python)
print([5*i**2-4 for i in range(1, 100)])
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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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