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A071289
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a(n) = n*(n^2 + 1) if n is even, otherwise (n - 1/2)*(n^2 + 1).
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0
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0, 1, 10, 25, 68, 117, 222, 325, 520, 697, 1010, 1281, 1740, 2125, 2758, 3277, 4112, 4785, 5850, 6697, 8020, 9061, 10670, 11925, 13848, 15337, 17602, 19345, 21980, 23997, 27030, 29341, 32800, 35425, 39338, 42297, 46692, 50005, 54910, 58597, 64040, 68121, 74130
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OFFSET
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0,3
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COMMENTS
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Sum of the numbers along the diagonals of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows (see example). - Wesley Ivan Hurt, May 15 2021
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REFERENCES
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T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
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LINKS
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Table of n, a(n) for n=0..42.
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
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FORMULA
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From R. J. Mathar, Oct 19 2010: (Start)
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
G.f.: x*(1 + 9*x + 12*x^2 + 16*x^3 + 7*x^4 + 3*x^5) / ( (1+x)^3*(x-1)^4 ). (End)
a(n) = (n^2+1)*(4*n-1+(-1)^n)/4. - Wesley Ivan Hurt, May 15 2021
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EXAMPLE
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From Wesley Ivan Hurt, May 15 2021: (Start)
[1 2 3 4 5]
[1 2 3 4] [6 7 8 9 10]
[1 2 3] [5 6 7 8] [11 12 13 14 15]
[1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
[1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
------------------------------------------------------------------------
n 1 2 3 4 5
------------------------------------------------------------------------
a(n) 1 10 25 68 117
------------------------------------------------------------------------
(End)
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MATHEMATICA
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Array[If[EvenQ[#], #(#^2+1), (#-1/2)(#^2+1)]&, 50, 0] (* Harvey P. Dale, Sep 20 2013 *)
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CROSSREFS
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Sequence in context: A137930 A251310 A251194 * A268303 A248833 A220039
Adjacent sequences: A071286 A071287 A071288 * A071290 A071291 A071292
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jun 12 2002
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STATUS
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approved
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