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A028884
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a(n) = (n + 3)^2 - 8.
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12
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1, 8, 17, 28, 41, 56, 73, 92, 113, 136, 161, 188, 217, 248, 281, 316, 353, 392, 433, 476, 521, 568, 617, 668, 721, 776, 833, 892, 953, 1016, 1081, 1148, 1217, 1288, 1361, 1436, 1513, 1592, 1673, 1756, 1841, 1928, 2017, 2108, 2201, 2296, 2393
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OFFSET
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0,2
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LINKS
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Altug Alkan, Table of n, a(n) for n = 0..10000
Patrick De Geest, Palindromic Quasipronics of the form n(n+x)
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = a(n-1) + 2*n + 5 (with a(0) = 1). - Vincenzo Librandi, Aug 05 2010
a(n) = A028560(n) + 1; A014616(n) = floor(a(n+1)/4). - Reinhard Zumkeller, Apr 07 2013
G.f.: ( -1 - 5*x + 4*x^2 ) / (x-1)^3. - R. J. Mathar, Mar 24 2013
Sum_{n >= 0} 1/a(n) = 51/112 - Pi*cot(2*Pi*sqrt(2))/(4*sqrt(2)) = 1.3839174974448... . - Vaclav Kotesovec, Apr 10 2016
E.g.f.: (1 + 7*x + x^2)*exp(x). - G. C. Greubel, Aug 19 2017
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EXAMPLE
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a(1) = 2*1 + 1 + 5 = 8; a(2) = 2*2 + 8 + 5 = 17; a(3) = 2*3 + 17 + 5 = 28. - Vincenzo Librandi, Aug 05 2010
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MATHEMATICA
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Range[3, 50]^2 - 8 (* Alonso del Arte, Aug 15 2016 *)
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PROG
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(Haskell)
a014616 n = (n * (n + 6) + 1) `div` 4 -- Reinhard Zumkeller, Apr 07 2013
(PARI) a(n)=(n+3)^2-8 \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Cf. A005563.
Sequence in context: A190749 A056121 A264355 * A247117 A099358 A077222
Adjacent sequences: A028881 A028882 A028883 * A028885 A028886 A028887
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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EXTENSIONS
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Definition corrected by Omar E. Pol, Jul 27 2009
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STATUS
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approved
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