A067330 -id:A067330 - cp's OEIS frontend

A067431 Convolution of Fibonacci F(n+1), n>=0, with F(n+8), n>=0.

21, 55, 131, 275, 550, 1058, 1985, 3653, 6625, 11875, 21084, 37140, 64989, 113075, 195775, 337507, 579650, 992182, 1693225, 2881825, 4892861, 8288915, 14013816, 23649000, 39841125, 67014703, 112558715

Offset: 0

Wolfdieter Lang, Feb 15 2002

Eighth diagonal of A067330. Eighth column of A067418.

a(n)= A067330(n+7, n) = A067418(n+7, 7) = sum(F(k+1)*F(n+8-k), k=0..n), n>=0.
G.f.: (21+13*x)/(1-x-x^2)^2.
a(n)= ((76*n+5*21)*F(n+1)+47*(n+1)*F(n))/5, F(n) := A000045(n) (Fibonacci); 21=F(8), 76=L(9), 47=L(8), L(n) := A000204(n) (Lucas).

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

Original entry on oeis.org

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

Wolfdieter Lang, Feb 15 2002

Tenth diagonal of A067330. Tenth column of A067418.

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).

cp's OEIS Frontend

A067431 Convolution of Fibonacci F(n+1), n>=0, with F(n+8), n>=0.

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