A017114 a(n) = (8*n + 4)^2.
16, 144, 400, 784, 1296, 1936, 2704, 3600, 4624, 5776, 7056, 8464, 10000, 11664, 13456, 15376, 17424, 19600, 21904, 24336, 26896, 29584, 32400, 35344, 38416, 41616, 44944, 48400, 51984, 55696, 59536, 63504, 67600, 71824, 76176, 80656, 85264, 90000, 94864, 99856
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[(8*n+4)^2: n in [0..35] ]; // Vincenzo Librandi, Jul 21 2011
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Mathematica
LinearRecurrence[{3, -3, 1},{16, 144, 400},30] (* Ray Chandler, Aug 04 2015 *) (8*Range[0,40]+4)^2 (* Harvey P. Dale, Aug 13 2024 *) -
PARI
a(n)=(8*n+4)^2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
From Paul Curtz, Nov 07 2008: (Start)
a(n) = 16*A016754(n).
a(n+2) = A061042(2n+1), from Brackett spectrum of hydrogen. (End)
G.f.: -16*(1 + 6*x + x^2)/(x-1)^3. - R. J. Mathar, Jul 14 2016
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = A017113(n)^2.
a(n) = 2^2*A016826(n).
Sum_{n>=0} 1/a(n) = Pi^2/128.
Sum_{n>=0} (-1)^n/a(n) = G/16, where G is Catalan's constant (A006752). (End)