OFFSET
1,2
COMMENTS
Integers k such that 3*k + 6 is a perfect square. - Gary Detlefs, Feb 22 2010
Binomial transform of (1, 9, 6, 0, 0, 0, 0, 0, 0, 0, ...). - Philippe Deléham, Mar 16 2014
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
A. J. C. Cunningham, Factorisation of N and N' = (x^n -+ y^n) / (x -+ y) [when x-y=n], Messenger Math., 54 (1924), 17-21 [Incomplete annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1)
FORMULA
a(n) = a(n-1) + 6*n - 3 for n>1. - Vincenzo Librandi, Nov 17 2010
G.f.: x*(1+7*x-2*x^2) / (1-x)^3. - R. J. Mathar, Oct 03 2011
-a(n) = (k-1)^2 + k^2 + (k+1)^2, where k = n*sqrt(-1). - Bruno Berselli, Jan 24 2014
a(T(n)+1) = T(n+1)^2 + T(n)^2 + T(n-1)^2, where T = A000217. - Bruno Berselli, May 14 2014
a(n+1) = binomial(n,0) + 9*binomial(n,1) + 6*binomial(n,2). - Philippe Deléham, Mar 16 2014
a(n) = floor(1/(n*tan(1/n) - 1)). - Clark Kimberling, Dec 02 2014
E.g.f.: 2 - (2 - 3*x - 3*x^2)*exp(x). - G. C. Greubel, Mar 27 2023
EXAMPLE
From Philippe Deléham, Mar 16 2014: (Start)
a(2)=10 after the evaluation of a(2) = 3*(2^2) - 2 = 3*(4) - 2 = 12 - 2 = 10.
a(1) = 1*1 = 1;
a(2) = 1*1 + 9*1 = 10;
a(3) = 1*1 + 9*2 + 6*1 = 25;
a(4) = 1*1 + 9*3 + 6*3 = 46;
a(5) = 1*1 + 9*4 + 6*6 = 73; etc. (End)
MATHEMATICA
3*Range[50]^2-2 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
CoefficientList[Series[x (1+7x-2x^2)/(1-x)^3, {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 1}, {1, 10, 25}, 50] (* Harvey P. Dale, Nov 20 2023 *)
PROG
(PARI) a(n)=3*n^2-2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [3*n^2-2: n in [1..50]]; // G. C. Greubel, Mar 27 2023
(SageMath) [3*n^2 -2 for n in range(1, 51)] # G. C. Greubel, Mar 27 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Tyler J Newman (Tylerjnewman(AT)adelphia.net), Nov 27 2004
STATUS
approved