A100536 a(n) = 3*n^2 - 2.
1, 10, 25, 46, 73, 106, 145, 190, 241, 298, 361, 430, 505, 586, 673, 766, 865, 970, 1081, 1198, 1321, 1450, 1585, 1726, 1873, 2026, 2185, 2350, 2521, 2698, 2881, 3070, 3265, 3466, 3673, 3886, 4105, 4330, 4561, 4798, 5041, 5290, 5545, 5806, 6073, 6346, 6625
Offset: 1
Examples
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)
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]
- John Elias, Illustration of Initial Terms: triple diamond configuration
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1)
Programs
-
Magma
[3*n^2-2: n in [1..50]]; // G. C. Greubel, Mar 27 2023
-
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 *)
-
PARI
a(n)=3*n^2-2 \\ Charles R Greathouse IV, Oct 07 2015
-
SageMath
[3*n^2 -2 for n in range(1,51)] # G. C. Greubel, Mar 27 2023
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
(3*n)^2 = a(n-1) + a(n) + a(n+1). - Nicolas Bělohoubek, Jul 02 2025
Comments