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 A283667 Number of Motzkin prefixes of length 2n and height n. 3
 1, 3, 13, 64, 334, 1802, 9933, 55575, 314362, 1793126, 10295625, 59430043, 344559826, 2005026610, 11703965955, 68503652100, 401892122682, 2362629703214, 13914547415998, 82081163986020, 484893156220356, 2868234297838092, 16986185485228431, 100703275233924096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1279 FORMULA Recursion: see Maple program. a(n) = A283595(2n,n). a(n) ~ sqrt(769 + 2762/sqrt(13)) * (70 + 2*13^(3/2))^n / (3^(3*n+3)*sqrt(3*Pi*n)). - Vaclav Kotesovec, Mar 13 2017 MAPLE a:= proc(n) option remember; `if`(n<2, 1+2*n, ((4*n-2)*(455*n^6-        1155*n^5-2776*n^4+1047*n^3+1493*n^2-72*n-72)*a(n-1)+36*       (n-1)*(2*n-1)*(2*n-3)*(13*n^4-7*n^3-64*n^2-44*n-6)*a(n-2))/       ((9*n+6)*(3*n+1)*(n+1)*(13*n^4-59*n^3+35*n^2+11*n-6)))     end: seq(a(n), n=0..30); CROSSREFS Cf. A283595, A283799. Sequence in context: A180111 A292183 A006923 * A011272 A200719 A065065 Adjacent sequences:  A283664 A283665 A283666 * A283668 A283669 A283670 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 13 2017 STATUS approved

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Last modified April 18 16:37 EDT 2019. Contains 322209 sequences. (Running on oeis4.)