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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 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

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