A213577 Principal diagonal of the convolution array A213576.

1, 4, 17, 56, 172, 498, 1395, 3820, 10307, 27534, 73064, 193012, 508341, 1336132, 3507189, 9197732, 24107124, 63159782, 165433895, 433246860, 1134484871, 2970509594, 7777554192, 20363014056, 53312938537, 139578241348

Offset: 1

Author

Clark Kimberling, Jun 18 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-6,-3,6,1,-1).

Crossrefs

Cf. A213576, A213500.

Programs

GAP

List([1..40], n-> Fibonacci(2*n+3) - Fibonacci(n+3) - n*Fibonacci(n+1)); # G. C. Greubel, Jul 05 2019

Magma

[Fibonacci(2*n+3) -Fibonacci(n+3) -n*Fibonacci(n+1): n in [1..40]]; // G. C. Greubel, Jul 05 2019

Mathematica

(See A213576.)
LinearRecurrence[{5,-6,-3,6,1,-1},{1,4,17,56,172,498},30] (* Harvey P. Dale, Aug 23 2012 *)
Table[Fibonacci[2n+3] -Fibonacci[n+3] -n*Fibonacci[n+1], {n,1,40}] (* G. C. Greubel, Jul 05 2019 *)

PARI

vector(40, n, fibonacci(2*n+3) - fibonacci(n+3) - n*fibonacci(n+1)) \\ G. C. Greubel, Jul 05 2019

Sage

[fibonacci(2*n+3) - fibonacci(n+3) - n*fibonacci(n+1) for n in (1..40)] # G. C. Greubel, Jul 05 2019

Formula

a(n) = 5*a(n-1) - 6*a(n-2) - 3*a(n-3) + 6*a(n-4) + a(n-5) - a(n-6).

G.f.: x*(1 - x + 3*x^2 - 2*x^3)/((1 - 3*x + x^2)*(1 - x - x^2)^2).

a(n) = Fibonacci(2*n+3) - Fibonacci(n+3) - n*Fibonacci(n+1). - G. C. Greubel, Jul 05 2019