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A116668
a(n) = (5*n^2 + n + 2)/2.
3
1, 4, 12, 25, 43, 66, 94, 127, 165, 208, 256, 309, 367, 430, 498, 571, 649, 732, 820, 913, 1011, 1114, 1222, 1335, 1453, 1576, 1704, 1837, 1975, 2118, 2266, 2419, 2577, 2740, 2908, 3081, 3259, 3442, 3630, 3823, 4021, 4224, 4432, 4645, 4863, 5086, 5314, 5547
OFFSET
0,2
COMMENTS
Binomial transform of (1, 3, 5, 0, 0, 0, ...).
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
Cf. A116666.
Sequence in context: A008212 A008080 A008157 * A225254 A008186 A008264
KEYWORD
nonn,easy,changed
AUTHOR
Gary W. Adamson, Feb 22 2006
EXTENSIONS
More terms from Emeric Deutsch, Feb 28 2006
STATUS
approved