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A233149
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a(n) = ((n^2+1)^3) - s, where s is the nearest square to (n^2+1)^3.
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0
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-1, 4, -24, 13, -113, 28, -316, 49, -681, 76, -1256, 109, -2089, 148, -3228, 193, -4721, 244, -6616, 301, -8961, 364, -11804, 433, -15193, 508, -19176, 589, -23801, 676, -29116, 769, -35169, 868, -42008, 973, -49681, 1084, -58236, 1201, -67721, 1324, -78184, 1453, -89673, 1588, -102236, 1729, -115921, 1876
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..50.
Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).
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FORMULA
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a(n) = (n^2+1)^3 - (round(sqrt((n^2+1)^3))^2.
Recurrence formula: a(n)= - a(n-2) + 4*a(n-4) - 6*a(n-6) + 4*a(n-8).
a(n) = -A077119(n^2+1). - R. J. Mathar, Jan 18 2021
a(2*n) = A056107(n). - R. J. Mathar, Jan 18 2021
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EXAMPLE
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Table of n, n^2, n^2+1, (n^2+1)^3, closest square, difference:
1 1 2 8 9 -1
2 4 5 125 121 4
3 9 10 1000 1024 -24
4 16 17 4913 4900 1
...
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MATHEMATICA
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aa = {}; Do[AppendTo[aa, (n^2 + 1)^3 - Round[Sqrt[(n^2 + 1)^3]]^2], {n, 1, 50}]; aa
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CROSSREFS
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Cf. A077119, A056107.
Sequence in context: A010294 A350887 A216923 * A169688 A222595 A103225
Adjacent sequences: A233146 A233147 A233148 * A233150 A233151 A233152
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KEYWORD
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sign,easy
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AUTHOR
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Artur Jasinski, Dec 05 2013
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STATUS
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approved
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