A213770 Antidiagonal sums of the convolution array A213768.

1, 7, 23, 58, 126, 250, 467, 837, 1457, 2484, 4172, 6932, 11429, 18739, 30603, 49838, 81002, 131470, 213175, 345425, 559461, 905832, 1466328, 2373288, 3840841, 6215455, 10057727, 16274722, 26334102, 42610594, 68946587, 111559197

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

Formula

a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5).

G.f.: f(x)/g(x), where f(x) = x*(1 + 3*x) and g(x) = (1 - x - x^2)(1 - x)^3.

a(n) = 2*Fibonacci(n+6) + Lucas(n+4) - n*(2*n + 11) - 23. - Ehren Metcalfe, Jul 08 2019

Mathematica

(See A213768.)

Prog

(Magma) [2*Fibonacci(n+6)+Lucas(n+4)-n*(2*n+11)-23: n in [1..35]]; // Vincenzo Librandi, Jul 09 2019

Crossrefs

Cf. A213768, A213500.

Sequence in context: A151718 A027918 A058195 * A235683 A037165 A126284

Adjacent sequences: A213767 A213768 A213769 * A213771 A213772 A213773

Keyword

nonn,easy

Author

Clark Kimberling, Jun 21 2012

Status

approved