

A099761


a(n) = ( n*(n+2) )^2.


6



0, 9, 64, 225, 576, 1225, 2304, 3969, 6400, 9801, 14400, 20449, 28224, 38025, 50176, 65025, 82944, 104329, 129600, 159201, 193600, 233289, 278784, 330625, 389376, 455625, 529984, 613089, 705600, 808201, 921600, 1046529, 1183744, 1334025
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OFFSET

0,2


COMMENTS

Using four consecutive triangular numbers t1, t2, t3, t4, form a 2 X 2 determinant with the first row t1 and t2 and the second row t3 and t4. Squaring the determinant gives the numbers in this sequence.  J. M. Bergot, May 17 2012
Numbers k such that sqrt(1 + sqrt(k)) is integer.  Jaroslav Krizek, Jan 23 2014


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

G.f.: x*(9 +19*x 5*x^2 +x^3)/(1x)^5.  R. J. Mathar, Apr 02 2011
a(n) = (A005563(n))^2.  Pedro Caceres, Aug 04 2019
E.g.f.: exp(x)*x*(9 + 23*x + 10*x^2 + x^3).  Stefano Spezia, Aug 05 2019
a(n) = (determinant [T(n1) T(n) ; T(n+1) T(n+2)])^2 where T is A000217.  J. M. Bergot, May 17 2012 and Bernard Schott, Aug 06 2019
From Amiram Eldar, Jul 13 2020: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/12  11/16.
Sum_{n>=1} (1)^(n+1)/a(n) = Pi^2/24  5/16. (End)


MAPLE

A099761 := proc(n) n^2*(n+2)^2 ; end proc:
seq(A099761(n), n=0..40) ; # R. J. Mathar, Apr 02 2011


MATHEMATICA

Table[1 2m^2 +m^4, {m, 40}] (* Artur Jasinski, Aug 15 2007 *)


PROG

(PARI) vector(40, n, (n^21)^2) \\ G. C. Greubel, Sep 03 2019
(MAGMA) [(n*(n+2))^2: n in [0..40]]; // G. C. Greubel, Sep 03 2019
(Sage) [(n*(n+2))^2 for n in (0..40)] # G. C. Greubel, Sep 03 2019
(GAP) List([0..40], n> (n*(n+2))^2); # G. C. Greubel, Sep 03 2019


CROSSREFS

Cf. A005563.
Sequence in context: A050792 A171671 A016886 * A018201 A181888 A000444
Adjacent sequences: A099758 A099759 A099760 * A099762 A099763 A099764


KEYWORD

nonn,easy


AUTHOR

Kari Lajunen (Kari.Lajunen(AT)Welho.com), Nov 11 2004


EXTENSIONS

Deleted a trivial formula which was based on another offset  R. J. Mathar, Dec 16 2009


STATUS

approved



