A016898 a(n) = (5*n + 4)^2.
16, 81, 196, 361, 576, 841, 1156, 1521, 1936, 2401, 2916, 3481, 4096, 4761, 5476, 6241, 7056, 7921, 8836, 9801, 10816, 11881, 12996, 14161, 15376, 16641, 17956, 19321, 20736, 22201, 23716, 25281, 26896, 28561, 30276, 32041, 33856, 35721, 37636, 39601, 41616
Offset: 0
Examples
a(0) = (5*0 + 4)^2 = 16.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Milan Janjic, Two Enumerative Functions.
- Eric Weisstein's MathWorld, Polygamma Function.
- Wikipedia, Polygamma Function.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[(5*n+4)^2: n in [0..70]]; // Vincenzo Librandi, May 02 2011
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Mathematica
Table[(5*n + 4)^2, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *) LinearRecurrence[{3,-3,1},{16,81,196},50] (* Harvey P. Dale, Jul 30 2023 *) -
PARI
Vec((16 + 33*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, Mar 30 2017
Formula
From Colin Barker, Mar 30 2017: (Start)
G.f.: (16 + 33*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
Sum_{n>=0} 1/a(n) = polygamma(1, 4/5)/25. - Amiram Eldar, Oct 02 2020
Comments