OFFSET
0,1
COMMENTS
Quadratic equation derived from the four primes 61, 67, 71, 73 using the method of common differences. Many of the initial terms are primes.
LINKS
Michael M. Ross, Natural Numbers.
Robert Sacks, Number Spiral: Method of Common Differences.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Arkadiusz Wesolowski, Oct 24 2013: (Start)
a(n) = -A186950(n+19).
G.f.: (53 - 98*x + 43*x^2)/(1 - x)^3. (End)
From Elmo R. Oliveira, Nov 02 2024: (Start)
E.g.f.: (53 + 8*x - x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
EXAMPLE
For n=8, -1*8^2 + 9*8 + 53 = 61.
MATHEMATICA
Table[ - n^2 + 9*n + 53, {n, 0, 46}] (* Arkadiusz Wesolowski, Oct 24 2013 *)
LinearRecurrence[{3, -3, 1}, {53, 61, 67}, 60] (* Harvey P. Dale, Apr 04 2024 *)
PROG
(PARI) a(n) = -n^2 + 9*n + 53 \\ Michel Marcus, Jun 30 2013
(Magma) [-n^2+9*n+53 : n in [0..46]]; // Arkadiusz Wesolowski, Oct 24 2013
CROSSREFS
KEYWORD
sign,easy,changed
AUTHOR
Michael M. Ross, Mar 13 2007
STATUS
approved