OFFSET
0,2
COMMENTS
Binomial transform of (1, 3, 5, 0, 0, 0, ...).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
Product of Pascal's triangle as an infinite lower triangular matrix and the vector (1, 3, 5, 0, 0, 0, ...).
O.g.f.: (1+x+3*x^2)/(1-x)^3. - R. J. Mathar, Apr 02 2008
a(n) = 5*n + a(n-1) - 2 (with a(0)=1) - Vincenzo Librandi, Nov 13 2010
From Elmo R. Oliveira, Oct 25 2024: (Start)
E.g.f.: exp(x)*(1 + 3*x + 5*x^2/2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
EXAMPLE
a(3) = 1*1 + 3*3 + 3*5 + 1*0 = 25.
MAPLE
a:=n->(5*n^2+n+2)/2: seq(a(n), n=0..50); # Emeric Deutsch, Feb 28 2006
MATHEMATICA
s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 235, 5}] lst (* Zerinvary Lajos, Jul 11 2009 *)
LinearRecurrence[{3, -3, 1}, {1, 4, 12}, 50] (* G. C. Greubel, Jan 29 2018 *)
PROG
(PARI) a(n)=(5*n^2+n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(5*n^2 + n+2)/2: n in [0..50]]; // G. C. Greubel, Jan 29 2018
(GAP) List([0..1000], n->(5*n^2+n+2)/2); # Muniru A Asiru, Jan 30 2018
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Gary W. Adamson, Feb 22 2006
EXTENSIONS
More terms from Emeric Deutsch, Feb 28 2006
STATUS
approved