A167614 a(n) = (n^2 + 3*n + 8)/2.

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, 1434, 1488, 1543

Offset: 1

Author

Vincenzo Librandi, Nov 07 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A016028, A027691, A152949, A152950, A228446.

Programs

Magma

[(n^2+3*n+8)/2: n in [1..60]]; // Vincenzo Librandi, Sep 16 2013

Mathematica

Table[(n(n+3))/2+4,{n,80}]  (* Harvey P. Dale, Mar 24 2011 *)
CoefficientList[Series[(6 - 9 x + 4 x^2)/(1 - x)^3,{x, 0, 60}], x] (* Vincenzo Librandi, Sep 16 2013 *)

PARI

a(n)=n*(n+3)/2+4 \\ Charles R Greathouse IV, Jan 11 2012

Python

print([n*(n+3)//2+4 for n in range(1, 60)]) # Gennady Eremin, Feb 03 2022

Formula

a(n) = n + a(n-1) + 1, with n > 1, a(1)=6.

G.f.: x*(6 - 9*x + 4*x^2)/(1-x)^3. - Vincenzo Librandi, Sep 16 2013

A228446(a(n)) = 7. - Reinhard Zumkeller, Mar 12 2014

a(n) = A152950(n+2) = A152949(n+3) = A016028(n+5). - Mathew Englander, Feb 03 2022

From Elmo R. Oliveira, Nov 15 2024: (Start)

E.g.f.: exp(x)*(4 + 2*x + x^2/2) - 4.

a(n) = A027691(n+1)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. (End)

Extensions

Corrected (changed one term from 1036 to 1038) by Harvey P. Dale, Mar 24 2011

New name from Charles R Greathouse IV, Jan 11 2012