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URL: https://oeis.org/A167614

⇱ A167614 - OEIS

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A167614
a(n) = (n^2 + 3*n + 8)/2.
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, 1434, 1488, 1543
OFFSET
1,1
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
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