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A201090 Number of -n..n arrays of 5 elements with first and second differences also in -n..n.

%I A201090 #9 Jul 22 2025 16:05:03
%S A201090 47,537,2771,9593,25935,59533,121371,226521,394443,649989,1023515,
%T A201090 1552101,2279419,3257221,4544919,6211381,8334179,11001745,14312231,
%U A201090 18376077,23314439,29262209,36365967,44787505,54701247,66298329,79783443
%N A201090 Number of -n..n arrays of 5 elements with first and second differences also in -n..n.
%C A201090 Row 5 of A201088
%H A201090 R. H. Hardin, <a href="/A201090/b201090.txt">Table of n, a(n) for n = 1..210</a>
%F A201090 Empirical: a(n) = 2*a(n-1) +2*a(n-2) -5*a(n-3) -2*a(n-4) +4*a(n-5) +4*a(n-6) -2*a(n-7) -5*a(n-8) +2*a(n-9) +2*a(n-10) -a(n-11).
%F A201090 Empirical: -x*(-47 -443*x -1603*x^2 -3212*x^3 -3986*x^4 -3218*x^5 -1606*x^6 -436*x^7 -47*x^8 -3*x^9 +x^10) / ( (1+x+x^2)*(1+x)^3*(x-1)^6 ). - R. J. Mathar, Nov 27 2011
%e A201090 Some solutions for n=6
%e A201090 ..0....1....3....5....2...-1....6...-2...-1...-4....5....2....6....5....4....5
%e A201090 ..4....0....0....2....3...-2....3....0...-5...-4....0...-3....0....2....2....1
%e A201090 ..5...-1....0...-3...-1...-4....0...-1...-6...-6....0...-3...-2....1....1...-2
%e A201090 ..2....3...-3...-4....1...-2....2...-1...-3...-4....0....1...-3....4...-3...-1
%e A201090 .-4....4...-4...-1....6...-6....5....1....1....0....0....5...-1....5...-2....4
%K A201090 nonn
%O A201090 1,1
%A A201090 _R. H. Hardin_ Nov 26 2011