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A083364
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Antidiagonal sums of table A083362.
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2
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1, 5, 17, 32, 71, 105, 187, 248, 389, 485, 701, 840, 1147, 1337, 1751, 2000, 2537, 2853, 3529, 3920, 4751, 5225, 6227, 6792, 7981, 8645, 10037, 10808, 12419, 13305, 15151, 16160, 18257, 19397, 21761, 23040, 25687, 27113, 30059, 31640, 34901, 36645
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OFFSET
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0,2
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COMMENTS
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A083362 is the square table of least distinct positive integers such that the sum of any two consecutive terms in any row form a square.
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LINKS
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FORMULA
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a(2n) = n(n+1)(4n+3)+(2n+1), a(2n+1) = ((n+1)^2)(4n+3)+(2n+2), for n>=0. - Paul D. Hanna, Apr 30 2003
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). - Colin Barker, Sep 26 2014
G.f.: (x^5+6*x^4+3*x^3+9*x^2+4*x+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Sep 26 2014
a(n) = (4*n^3+12*n^2+18*n+9+(2*n^2+2*n-1)*(-1)^n)/8. - Wesley Ivan Hurt, Sep 26 2014
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MAPLE
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MATHEMATICA
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Table[(4 n^3 + 12 n^2 + 18 n + 9 + (2 n^2 + 2 n - 1) (-1)^n)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Sep 26 2014 *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 5, 17, 32, 71, 105, 187}, 50] (* Harvey P. Dale, Aug 16 2021 *)
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PROG
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(PARI) Vec((x^5+6*x^4+3*x^3+9*x^2+4*x+1)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 26 2014
(Magma) [(4*n^3+12*n^2+18*n+9+(2*n^2+2*n-1)*(-1)^n)/8 : n in [0..40]]; // Wesley Ivan Hurt, Sep 26 2014
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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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