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URL: https://oeis.org/A179992

⇱ A179992 - OEIS

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A179992
a(n) = a(n-1) + a(n-2) + n^2 for n >= 3, a(1)=2, and a(2)=5.
0
2, 5, 16, 37, 78, 151, 278, 493, 852, 1445, 2418, 4007, 6594, 10797, 17616, 28669, 46574, 75567, 122502, 198469, 321412, 520365, 842306, 1363247, 2206178, 3570101, 5777008, 9347893, 15125742, 24474535, 39601238, 64076797, 103679124
OFFSET
1,1
COMMENTS
Each term is the sum of the previous two plus the square of its index.
FORMULA
a(n) = F(n-2) + (Sum_{i=1..n} i^2) + Sum_{k=0..n-2} F(k)*Sum_{j=0..n-k-1} j^2, where F(i) is the i-th Fibonacci number. [Corrected by Jason Yuen, Apr 09 2025]
G.f.: x*(x^4-4*x^3+6*x^2-3*x+2)/((1-x-x^2)*(1-x)^3). [Corrected by Bruno Berselli, Aug 25 2010 and R. J. Mathar, Oct 18 2010]
Limiting ratio a(n+1)/a(n) = Phi = 1.618038...
a(n) = 2*A022095(n+2)-6*n-13-n^2. - R. J. Mathar, Aug 06 2010
a(n)-4*a(n-1)+5*a(n-2)-a(n-3)-2*a(n-4)+a(n-5) = 0 with n>5. - Bruno Berselli, Aug 25 2010
EXAMPLE
a(5) = a(4)+a(3)+5^2 = 16+37+25 = 78.
CROSSREFS
Cf. A160536, A163250. - Bruno Berselli, Aug 25 2010
Sequence in context: A053683 A305876 A082085 * A054971 A124720 A188947
KEYWORD
nonn,easy
AUTHOR
Carmine Suriano, Aug 05 2010
STATUS
approved