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A082297
Main diagonal of array A083861.
1
0, 1, 5, 22, 105, 551, 3125, 18901, 120785, 809956, 5669525, 41253125, 310968905, 2421594449, 19434554165, 160416509794, 1359425390625, 11809173506531, 105013666399445, 954781355707373, 8865807366284825, 83996265859375000, 811222567266570805, 7980019803318567233
OFFSET
0,3
FORMULA
a(n) = (((5 + sqrt(4*n + 1))/2)^n - ((5 - sqrt(4*n + 1))/2)^n)/sqrt(4*n + 1).
MAPLE
T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := 5*T(n, k - 1) + (n - 6)*T(n, k - 2); end if; v; end proc;
seq(T(n, n), n = 0..40); # Petros Hadjicostas, Dec 25 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 06 2003
STATUS
approved