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 and 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 and 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 *)
PROG
(PARI) catalan(n) = binomial(2*n, n)/(n+1);
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*catalan(k+1)) % 8; \\ Michel Marcus, May 23 2022
CROSSREFS
KEYWORD
nonn,hear
AUTHOR
N. J. A. Sloane, Mar 16 2018
STATUS
approved