A067978 Convolution of Fibonacci F(n+1), n>=0, with F(n+10), n>=0.

55, 144, 343, 720, 1440, 2770, 5197, 9564, 17345, 31090, 55200, 97236, 170147, 296040, 512555, 883620, 1517568, 2597606, 4432985, 7544820, 12809845, 21700934, 36689088, 61914600, 104306575, 175448640

Offset: 0

Author

Wolfdieter Lang, Feb 15 2002

Keywords

• nonn
• easy

Comments

Tenth diagonal of A067330. Tenth column of A067418.

Formula

a(n)= A067330(n+9, n) = A067418(n+9, 9) = sum(F(k+1)*F(n+10-k), k=0..n), n>=0.

G.f.: (55+34*x)/(1-x-x^2)^2.

a(n)= ((199*n+5*55)*F(n+1)+123*(n+1)*F(n))/5, F(n) := A000045(n) (Fibonacci); 55=F(10), 123=L(10), 199=L(11), L(n) := A000204(n) (Lucas).