A152949 a(n) = 3 + binomial(n-1,2).

3, 3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, 949, 993, 1038, 1084, 1131, 1179, 1228, 1278, 1329, 1381

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 15 2008

Keywords

• nonn
• easy

Comments

a(1)=3; then add 0 to the first number, then 1,2,3,4,... and so on.

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A016028, A152947, A000124, A152948, A152950.

Programs

GAP

List([1..55],n->3+Binomial(n-1,2)); # Muniru A Asiru, Oct 28 2018

Maple

seq(coeff(series(x*(4*x^2-6*x+3)/(1-x)^3,x,n+1), x, n), n = 1 .. 55); # Muniru A Asiru, Oct 28 2018

Mathematica

s=3;lst={3};Do[s+=n;AppendTo[lst,s],{n,0,5!}];lst
Table[Binomial[n-1,2],{n,60}]+3 (* Harvey P. Dale, Feb 27 2013 *)

PARI

Vec( x*(3-6*x+4*x^2)/(1-x)^3 + O(x^66) ) \\ Joerg Arndt, Jul 24 2013

Sage

[3+binomial(n,2) for n in range(0, 54)] # Zerinvary Lajos, Mar 12 2009

Formula

a(n) = a(n-1) + n - 2 (with a(1)=3). - Vincenzo Librandi, Nov 27 2010

G.f.: x*(3-6*x+4*x^2)/(1-x)^3. - Nikita Gogin, Jul 24 2013

a(n) = A016028(n+1) for n >= 2. - Georg Fischer, Oct 28 2018

Sum_{n>=1} 1/a(n) = 1/3 + 2*Pi*tanh(sqrt(23)*Pi/2)/sqrt(23). - Amiram Eldar, Dec 13 2022