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 A027286 a(n) = Sum_{k=0..2n} (k+1) * A026584(n, k). 17
 1, 4, 18, 56, 190, 564, 1722, 4976, 14454, 40940, 115698, 322728, 896558, 2471588, 6786090, 18537184, 50459366, 136844892, 370030434, 997705240, 2683514526, 7201203988, 19284880794, 51546789456, 137541880150, 366412976332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,7,-8,-16). FORMULA G.f.: (1+2*x+3*x^2)/(1-x-4*x^2)^2. From G. C. Greubel, Dec 12 2021: (Start) a(n) = 2^(n-3)*( -6*Fibonacci(n+1, 1/2) + Sum_{j=0..n} Fibonacci(n-j+1, 1/2)*( 14*Fibonacci(j+1, 1/2) + 5*Fibonacci(j, 1/2) ), where Fibonacci(n, x) are the Fibonacci polynomials. a(n) = (2^(n-1)/17)*(n+1)*( 14*LucasL(n+2, 1/2) + 5*LucasL(n+1, 1/2) ), where L(n, x) are the Lucas polynomials. a(n) = 2*a(n-1) + 7*a(n-2) - 8*a(n-3) - 16*a(n-4). (End) MATHEMATICA LinearRecurrence[{2, 7, -8, -16}, {1, 4, 18, 56}, 30] (* G. C. Greubel, Dec 12 2021 *) PROG (Magma) I:=[1, 4, 18, 56]; [n le 4 select I[n] else 2*Self(n-1) +7*Self(n-2) -8*Self(n-3) -16*Self(n-4): n in [1..31]]; // G. C. Greubel, Dec 12 2021 (Sage) [2^(n-1)*(n+1)*(14*lucas_number2(n+2, 1/2, -1) + 5*lucas_number2(n+1, 1/2, -1))/17 for n in (0..30)] # G. C. Greubel, Dec 12 2021 (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -16, -8, 7, 2]^n*[1; 4; 18; 56])[1, 1] \\ Charles R Greathouse IV, Oct 21 2022 CROSSREFS Cf. A006131, A026584, A072265. Sequence in context: A181411 A238915 A212680 * A119044 A058851 A167885 Adjacent sequences: A027283 A027284 A027285 * A027287 A027288 A027289 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 20 22:04 EDT 2023. Contains 361391 sequences. (Running on oeis4.)