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

1,2

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).

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

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 *)

Prog

(PARI) vector(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
(Sage) [fibonacci(2*n+3) - fibonacci(n+3) - n*fibonacci(n+1) for n in (1..40)] # G. C. Greubel, Jul 05 2019
(GAP) List([1..40], n-> Fibonacci(2*n+3) - Fibonacci(n+3) - n*Fibonacci(n+1)) # G. C. Greubel, Jul 05 2019

Crossrefs

Cf. A213576, A213500.

Sequence in context: A060262 A157492 A108140 * A255526 A264218 A121327

Adjacent sequences: A213574 A213575 A213576 * A213578 A213579 A213580

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2012

Status

approved