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A014771
Squares of odd hexagonal numbers.
1
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
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
KEYWORD
nonn,easy
EXTENSIONS
More terms from Erich Friedman
STATUS
approved