

A179992


Extended three term Fibonacci sequence a(n)=a(n1)+a(n2)+n^2. a(1)=2; 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
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OFFSET

1,1


COMMENTS

Each term is the sum of the previous two plus the square of its index.


LINKS

Table of n, a(n) for n=1..33.
Index entries for linear recurrences with constant coefficients, signature (4,5,1,2,1).


FORMULA

a(n)=F(n)+sum(i^2; i=1 to n)+sum(F(k)*sum(j^2; j=0 to nk1); k=0 to n3)).
G.f.: x*(x^44*x^3+6*x^23*x+2)/((1xx^2)*(1x)^3)
Limiting ratio a(n+1)/a(n)=Phi=1.618038...
a(n) = 2*A022095(n+2)6*n13n^2. [From R. J. Mathar, Aug 06 2010]
a(n)4*a(n1)+5*a(n2)a(n3)2*a(n4)+a(n5) = 0 with n>5. [From Bruno Berselli, Aug 25 2010]


EXAMPLE

a(5)=a(4)+a(3)+5^2=16+37+25=78


CROSSREFS

Cf. A000045, A179991
Cf. A160536, A163250. [From Bruno Berselli, Aug 25 2010]
Sequence in context: A053683 A305876 A082085 * A054971 A124720 A188947
Adjacent sequences: A179989 A179990 A179991 * A179993 A179994 A179995


KEYWORD

nonn


AUTHOR

Carmine Suriano, Aug 05 2010


EXTENSIONS

Denominator of the g.f. replaced with product of factors by Bruno Berselli, Aug 25 2010
Multiplied g.f. with x to match the offset  R. J. Mathar, Oct 18 2010


STATUS

approved



