A203009
(n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(0)=2.
Original entry on oeis.org
1, 3, 11, 50, 374, 4282, 78924, 2322060, 110101476, 8413051008, 1038251025216, 207035781419520, 66749863269991104, 34803836775900988992, 29353783726459293724224, 40050488883338399323186560, 88407698594458813846355350656
Offset: 1
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f[k_] := LucasL[k - 1]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A203009 *)
A242496
a(n)=sum_{j=0..n} sum_{i=0..j} F(i)*L(j), where F(n)=A000045(n) and L(n)=A000032(n).
Original entry on oeis.org
0, 1, 7, 23, 72, 204, 564, 1521, 4059, 10747, 28336, 74504, 195576, 512865, 1344063, 3521007, 9221688, 24148468, 63230860, 165555665, 433454835, 1134839091, 2971111392, 7778574288, 20364739632, 53315851969, 139583151799, 365434146311, 956720165544
Offset: 0
For n=5, 0*(2+1+3+4+7+11) + 1*(1+3+4+7+11) + 1*(3+4+7+11) + 2*(4+7+11) + 3*(7+11) + 5*11 = 204 = F(2*5+3) - L(n+2) + 0 = 233-29 = 204.
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A242496 := proc(n)
add(add(A000045(i)*A000032(j),i=0..j),j=0..n) ;
end proc: # R. J. Mathar, May 17 2014
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LinearRecurrence[{4,-2,-6,4,2,-1},{0,1,7,23,72,204},30] (* Harvey P. Dale, Oct 03 2020 *)
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F(n) = fibonacci(n)
L(n) = if(n==0, 2, F(2*n)/F(n))
vector(30, n, sum(i=0, n-1, sum(j=i, n-1, F(i)*L(j)))) \\ Colin Barker, May 16 2014
Two terms corrected, and more terms added by
Colin Barker, May 16 2014
A242558
a(n) = Sum_{j=0..n} Sum_{i=0..j} L(i)*F(j) where L(i)=A000032(i) and F(j)=A000045(j).
Original entry on oeis.org
0, 3, 9, 29, 80, 220, 588, 1563, 4125, 10857, 28512, 74792, 196040, 513619, 1345281, 3522981, 9224880, 24153636, 63239220, 165569195, 433476725, 1134874513, 2971168704, 7778667024, 20364889680, 53316094755, 139583544633, 365434781933
Offset: 0
For n=5, a(n) = F(2*5+3) - F(5+2) - 0 = 233 - 13 = 220.
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LinearRecurrence[{4,-2,-6,4,2,-1},{0,3,9,29,80,220},30] (* Harvey P. Dale, Aug 15 2016 *)
Showing 1-3 of 3 results.
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