OFFSET
0,1
COMMENTS
Bisection of A000125.
This sequence is related to A002061 by a(n) = (n+1)*A002061(n+1) + Sum_{i=0..n} A002061(i). - Bruno Berselli, Dec 19 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = a(n-1) + (2*n)^2 + 2. - Philippe Deléham, Jan 18 2012
From Vincenzo Librandi, Jun 26 2012: (Start)
G.f.: 2*(1+3*x^2)/(1-x)^4;
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
From G. C. Greubel, Apr 03 2023: (Start)
a(n) = 2 + 2*A037237(n-1).
E.g.f.: (2/3)*(3 + 9*x + 9*x^2 + 2*x^3)*exp(x). (End)
MATHEMATICA
CoefficientList[Series[2*(1+3x^2)/((1-x)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {2, 8, 26, 64}, 40] (* Harvey P. Dale, Dec 27 2015 *)
PROG
(PARI) a(n)=n*(4*n^2+6*n+8)/3+2 \\ Charles R Greathouse IV, Jan 18 2012
(Magma) I:=[2, 8, 26, 64]; [n le 4 select I[n] else 4*Self(n-1) -6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 26 2012
(SageMath) [2 + 2*n*(2*n^2+3*n+4)/3 for n in range(41)] # G. C. Greubel, Apr 03 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 24 2004
EXTENSIONS
More terms from Hugo Pfoertner, Nov 25 2004
New name based on formula from Ralf Stephan
STATUS
approved