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 A299918 Motzkin numbers (A001006) mod 8. 9
 1, 1, 2, 4, 1, 5, 3, 7, 3, 3, 4, 6, 7, 3, 2, 4, 3, 3, 6, 4, 3, 7, 7, 7, 5, 5, 4, 2, 1, 5, 3, 7, 3, 3, 6, 4, 3, 7, 1, 5, 1, 1, 4, 2, 5, 1, 4, 6, 5, 5, 2, 4, 5, 1, 1, 1, 3, 3, 4, 6, 7, 3, 2, 4, 3, 3, 6, 4, 3, 7, 1, 5, 1, 1, 4, 2, 5, 1, 6, 4, 1, 1, 2, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 S.-P. Eu, S.-C. Liu, and Y.-N. Yeh, Catalan and Motzkin numbers modulo 4 and 8, Europ. J. Combin. 29 (2008), 1449-1466. Christian Krattenthaler, Thomas W. Müller, Motzkin numbers and related sequences modulo powers of 2, arXiv:1608.05657 [math.CO], 2016-2018. E. Rowland and R. Yassawi, Automatic congruences for diagonals of rational functions, J. Théorie Nombres Bordeaux 27 (2015), 245-288. Ying Wang, Guoce Xin, A Classification of Motzkin Numbers Modulo 8, Electron. J. Combin., 25(1) (2018), #P1.54. MAPLE f:= rectoproc({(3+3*n)*a(n)+(5+2*n)*a(1+n)+(-4-n)*a(n+2), a(0) = 1, a(1) = 1}, a(n), remember): seq(f(n) mod 8, n=0..200); # Robert Israel, Mar 16 2018 MATHEMATICA Table[Mod[GegenbauerC[n, -n - 1, -1/2] / (n + 1), 8], {n, 0, 100}] (* Vincenzo Librandi, Sep 08 2018 *) CROSSREFS Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710. Sequence in context: A060370 A318704 A165064 * A021418 A283741 A094640 Adjacent sequences:  A299915 A299916 A299917 * A299919 A299920 A299921 KEYWORD nonn,hear AUTHOR N. J. A. Sloane, Mar 16 2018 STATUS approved

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Last modified January 24 03:42 EST 2019. Contains 319412 sequences. (Running on oeis4.)