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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
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
Sequence in context: A060262 A157492 A108140 * A255526 A264218 A121327
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 18 2012
STATUS
approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)