OFFSET
0,1
COMMENTS
Numbers m such that m + 21 is a square. The product of two consecutive terms belongs to the sequence, see formula. - Klaus Purath, Oct 30 2022
REFERENCES
V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n^2 - 16*n + 43.
From Colin Barker, Nov 12 2014: (Start)
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: (43 -101*x + 60*x^2)/(1-x)^3. (End)
E.g.f.: (43 - 15*x + x^2)*exp(x). - G. C. Greubel, Aug 12 2019
From Klaus Purath, Oct 30 2022: (Start)
According to the formula a(n) = n^2 - 16*n + 43 when expanded to negative indices, a(n)*a(n+1) = a(a(n)+n) = (a(n)+n)*(a(n+1)-(n+1)) + 43.
a(n) = 2*a(n-1) - a(n-2) + 2. (End)
MAPLE
seq((n-8)^2 -21, n=0..60); # G. C. Greubel, Aug 12 2019
MATHEMATICA
CoefficientList[Series[(60x^2 -101x +43)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Nov 12 2014 *)
(Range[0, 60] -8)^2 -21 (* G. C. Greubel, Aug 12 2019 *)
PROG
(PARI) Vec(-(60*x^2-101*x+43)/(x-1)^3 + O(x^60)) \\ Colin Barker, Nov 12 2014
(Magma) [n^2-16*n+43: n in [0..60]]; // Vincenzo Librandi, Nov 12 2014
(Sage) [(n-8)^2 -21 for n in (0..60)] # G. C. Greubel, Aug 12 2019
(GAP) List([0..60], n-> (n-8)^2 -21); # G. C. Greubel, Aug 12 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Mar 24 2007
STATUS
approved