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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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)

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 *)

Prog

(PARI) a(n)=n*(n+3)/2+4 \\ Charles R Greathouse IV, Jan 11 2012
(Magma) [(n^2+3*n+8)/2: n in [1..60]]; // Vincenzo Librandi, Sep 16 2013
(Python)
print([n*(n+3)//2+4 for n in range(1, 60)]) # Gennady Eremin, Feb 03 2022

Crossrefs

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

Sequence in context: A315963 A315964 A315965 * A020751 A315966 A315967

Adjacent sequences: A167611 A167612 A167613 * A167615 A167616 A167617

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 07 2009

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

Status

approved