A213767 Antidiagonal sums of the convolution array A213765.
1, 5, 17, 47, 114, 254, 533, 1071, 2083, 3951, 7348, 13452, 24313, 43481, 77077, 135615, 237094, 412234, 713325, 1229155, 2110151, 3610655, 6159912, 10481112, 17790769, 30132269, 50933273, 85936271, 144750618, 243438806
Offset: 1
Links
- Clark Kimberling, Table of n, a(n) for n = 1..500
- Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,4,0,-1).
Programs
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Mathematica
(See A213765.)
Formula
a(n) = 4*a(n-1)-4*a(n-2)-2*a(n-3)+4*a(n-4)-a(n-6).
G.f.: f(x)/g(x), where f(x) = x*(1 + x + x^2 + x^3) and g(x) = (1 - 2*x + x^3)^2.
a(n) = n*Fibonacci(n+5) - Lucas(n+6) + 2*(2*n+9). - Ehren Metcalfe, Jul 10 2019