A014771 Squares of odd hexagonal numbers.
1, 225, 2025, 8281, 23409, 53361, 105625, 189225, 314721, 494209, 741321, 1071225, 1500625, 2047761, 2732409, 3575881, 4601025, 5832225, 7295401, 9018009, 11029041, 13359025, 16040025, 19105641, 22591009, 26532801, 30969225, 35940025, 41486481, 47651409
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[(2*n-1)^2*(4*n-3)^2 : n in [1..50]]; // Wesley Ivan Hurt, Jul 31 2016
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Maple
A014771:=n->(2*n-1)^2*(4*n-3)^2: seq(A014771(n), n=1..50); # Wesley Ivan Hurt, Jul 31 2016
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Mathematica
(Select[Table[n(2n-1), {n,60}], OddQ])^2 (* or *) LinearRecurrence[ {5,-10,10,-5,1}, {1,225,2025,8281,23409}, 30] (* Harvey P. Dale, Jun 23 2011 *)
Formula
G.f.: x*(1+220*x+910*x^2+396*x^3+9*x^4)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by R. J. Mathar, Sep 16 2009
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. - Harvey P. Dale, Jun 23 2011
a(n) = (2*n-1)^2*(4*n-3)^2. - Wesley Ivan Hurt, Jul 31 2016
Sum_{n>=1} 1/a(n) = 2*G + 3*Pi^2/8 - Pi - 2*log(2), where G is Catalan's constant (A006752). - Amiram Eldar, Feb 27 2022
Extensions
More terms from Erich Friedman