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 A179992 Extended three term Fibonacci sequence a(n)=a(n-1)+a(n-2)+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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Each term is the sum of the previous two plus the square of its index. LINKS 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 n-k-1); k=0 to n-3)). G.f.: x*(x^4-4*x^3+6*x^2-3*x+2)/((1-x-x^2)*(1-x)^3) Limiting ratio a(n+1)/a(n)=Phi=1.618038... a(n) = 2*A022095(n+2)-6*n-13-n^2. [From 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. [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

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Last modified March 28 11:00 EDT 2020. Contains 333083 sequences. (Running on oeis4.)