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A094260
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Sum of next n numbers/n if n divides the sum else n times the sum of next n numbers.
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0
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1, 10, 5, 136, 13, 666, 25, 2080, 41, 5050, 61, 10440, 85, 19306, 113, 32896, 145, 52650, 181, 80200, 221, 117370, 265, 166176, 313, 228826, 365, 307720, 421, 405450, 481, 524800, 545, 668746, 613, 840456, 685, 1043290, 761, 1280800, 841, 1556730, 925, 1875016, 1013, 2239786
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OFFSET
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1,2
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,0,1).
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FORMULA
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For even n, a(n) = A000217(n^2) = n^2*(n^2+1)/2; for odd n, a(n) = (n^2 + 1)/2.
Sum_{n>=1} 1/a(n) = 1 + Pi^2/12 - Pi*cosech(Pi). - Amiram Eldar, Aug 23 2022
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EXAMPLE
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The sequence is: 1/1, (2+3)*2, (4+5+6)/3, (7+8+9+10)*4, ...
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MATHEMATICA
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LinearRecurrence[{0, 5, 0, -10, 0, 10, 0, -5, 0, 1}, {1, 10, 5, 136, 13, 666, 25, 2080, 41, 5050}, 50] (* Harvey P. Dale, May 01 2020 *)
fix[c_]:=If[Mod[Total[c], Length[c]]==0, Total[c]/Length[c], Length[c] Total[c]]; fix/@With[ {nn=50}, TakeList[ Range[(nn(nn+1))/2], Range[nn]]] (* Harvey P. Dale, Apr 05 2023 *)
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PROG
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(PARI) a(n) = if (n%2, (n^2+1)/2, n^2*(n^2+1)/2); \\ Michel Marcus, Aug 23 2022
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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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