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A179992
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a(n) = a(n-1) + a(n-2) + n^2 for n >= 3, a(1)=2, and a(2)=5.
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0
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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
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1,1
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COMMENTS
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Each term is the sum of the previous two plus the square of its index.
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LINKS
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FORMULA
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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)).
Limiting ratio a(n+1)/a(n) = Phi = 1.618038...
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]
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EXAMPLE
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a(5) = a(4)+a(3)+5^2 = 16+37+25 = 78.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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