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 an 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)/(1-x)^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(n-1) 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^2-1)^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
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