A023550 Convolution of natural numbers >= 2 and (F(2), F(3), F(4), ...).

2, 7, 16, 32, 59, 104, 178, 299, 496, 816, 1335, 2176, 3538, 5743, 9312, 15088, 24435, 39560, 64034, 103635, 167712, 271392, 439151, 710592, 1149794, 1860439, 3010288, 4870784, 7881131, 12751976, 20633170, 33385211, 54018448, 87403728, 141422247, 228826048

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 1).

Formula

a(n) = A023537(n) + 2*n.

From Colin Barker, Mar 11 2017: (Start)

G.f.: x*(2-x)*(1+x) / ((1-x)^2*(1-x-x^2)).

a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-15+7*sqrt(5)) + (1+sqrt(5))^n*(15+7*sqrt(5)))) / sqrt(5) - 2*n - 7.

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

(End)

a(n) = Lucas(n+4) - 2*n - 7. - G. C. Greubel, Jun 01 2019

Mathematica

LinearRecurrence[{3, -2, -1, 1}, {2, 7, 16, 32}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)

Prog

(PARI) Vec(x*(2-x)*(1+x)/((1-x)^2*(1-x-x^2)) + O(x^40)) \\ Colin Barker, Mar 11 2017
(PARI) vector(40, n, fibonacci(n+5) + fibonacci(n+3) -2*n-7) \\ G. C. Greubel, Jun 01 2019
(Magma) [Lucas(n+4) - 2*n - 7 : n in [1..40]]; // G. C. Greubel, Jun 01 2019
(Sage) [lucas_number2(n+4, 1, -1) -2*n-7 for n in (1..40)] # G. C. Greubel, Jun 01 2019
(GAP) List([1..40], n-> Lucas(1, -1, n+4)[2] -2*n-7 ) # G. C. Greubel, Jun 01 2019

Crossrefs

Cf. A000032, A023537.

Sequence in context: A074470 A216499 A228189 * A332232 A333395 A130869

Adjacent sequences: A023547 A023548 A023549 * A023551 A023552 A023553

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved