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

1,2

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).

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

Mathematica

(See A213765.)

Crossrefs

Cf. A213765, A213500.

Sequence in context: A332358 A011853 A215053 * A320854 A136303 A268783

Adjacent sequences: A213764 A213765 A213766 * A213768 A213769 A213770

Keyword

nonn,easy

Author

Clark Kimberling, Jun 21 2012

Status

approved