A116668 a(n) = (5*n^2 + n + 2)/2.

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

Author

Gary W. Adamson, Feb 22 2006

Keywords

• nonn
• easy

Comments

Binomial transform of (1, 3, 5, 0, 0, 0, ...).

Examples

			a(3) = 1*1 + 3*3 + 3*5 + 1*0 = 25.
		

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).

Crossrefs

Cf. A116666.

Programs

GAP

List([0..1000],n->(5*n^2+n+2)/2); # Muniru A Asiru, Jan 30 2018

Magma

[(5*n^2 + n+2)/2: n in [0..50]]; // G. C. Greubel, Jan 29 2018

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 *)

PARI

a(n)=(5*n^2+n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

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)

Extensions

More terms from Emeric Deutsch, Feb 28 2006