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

1,2

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).

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

Maple

A014771:=n->(2*n-1)^2*(4*n-3)^2: seq(A014771(n), n=1..50); # Wesley Ivan Hurt, Jul 31 2016

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 *)

Prog

(Magma) [(2*n-1)^2*(4*n-3)^2 : n in [1..50]]; // Wesley Ivan Hurt, Jul 31 2016

Crossrefs

Cf. A003215, (hex numbers), A014634 (odd hex numbers), A006752.

Sequence in context: A076395 A203829 A105925 * A184878 A134741 A110204

Adjacent sequences: A014768 A014769 A014770 * A014772 A014773 A014774

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman

Status

approved