A006222 11*n^2 + 11*n + 3. (Formerly M3109)

3, 25, 69, 135, 223, 333, 465, 619, 795, 993, 1213, 1455, 1719, 2005, 2313, 2643, 2995, 3369, 3765, 4183, 4623, 5085, 5569, 6075, 6603, 7153, 7725, 8319, 8935, 9573, 10233, 10915, 11619, 12345, 13093, 13863, 14655, 15469, 16305

Offset

0,1

References

G. V. Chudnovsky, Transcendental numbers, pp. 45-69 of Number Theory Carbondale 1979, Lect. Notes Math. 751 (1982).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.:(3+16*x+3*x^2)/(1-x)^3. - Vincenzo Librandi, Jul 07 2012

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 07 2012

Maple

A006222:=-(3+16*z+3*z**2)/(z-1)**3; [Simon Plouffe in his 1992 dissertation.]

Mathematica

CoefficientList[Series[(3+16*x+3*x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)

Prog

(Magma) I:=[3, 25, 69]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012
(PARI) a(n)=11*n^2+11*n+3 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A041897 A356594 A242974 * A290165 A129443 A083298

Adjacent sequences: A006219 A006220 A006221 * A006223 A006224 A006225

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved