login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213577 Principal diagonal of the convolution array A213576. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)