cp's OEIS Frontend

A212787 Half the number of 0..n arrays of length 8 with second differences nonzero.

%I A212787 #8 Jul 22 2025 22:57:53
%S A212787 34,973,15490,103391,504337,1849215,5741427,15287517,36930573,
%T A212787 81191087,167048183,322740017,594609571,1046606337,1778111533,
%U A212787 2918485227,4659291144,7241632621,11008136317,16375938194,23924161904,34337250191
%N A212787 Half the number of 0..n arrays of length 8 with second differences nonzero.
%C A212787 Row 6 of A212782
%H A212787 R. H. Hardin, <a href="/A212787/b212787.txt">Table of n, a(n) for n = 1..210</a>
%F A212787 Empirical: a(n) = -2*a(n-1) -4*a(n-2) -4*a(n-3) -2*a(n-4) +4*a(n-5) +13*a(n-6) +21*a(n-7) +25*a(n-8) +18*a(n-9) +2*a(n-10) -24*a(n-11) -46*a(n-12) -61*a(n-13) -55*a(n-14) -33*a(n-15) +2*a(n-16) +38*a(n-17) +60*a(n-18) +68*a(n-19) +55*a(n-20) +39*a(n-21) +18*a(n-22) +10*a(n-23) +a(n-24) -2*a(n-25) -17*a(n-26) -39*a(n-27) -65*a(n-28) -88*a(n-29) -87*a(n-30) -69*a(n-31) -23*a(n-32) +23*a(n-33) +69*a(n-34) +87*a(n-35) +88*a(n-36) +65*a(n-37) +39*a(n-38) +17*a(n-39) +2*a(n-40) -a(n-41) -10*a(n-42) -18*a(n-43) -39*a(n-44) -55*a(n-45) -68*a(n-46) -60*a(n-47) -38*a(n-48) -2*a(n-49) +33*a(n-50) +55*a(n-51) +61*a(n-52) +46*a(n-53) +24*a(n-54) -2*a(n-55) -18*a(n-56) -25*a(n-57) -21*a(n-58) -13*a(n-59) -4*a(n-60) +2*a(n-61) +4*a(n-62) +4*a(n-63) +2*a(n-64) +a(n-65)
%e A212787 Some solutions for n=5
%e A212787 ..0....0....3....0....0....3....0....3....0....3....0....0....3....3....3....3
%e A212787 ..0....0....0....0....3....3....0....0....3....3....0....0....3....3....3....0
%e A212787 ..2....4....0....4....2....0....5....3....3....4....1....2....1....4....1....0
%e A212787 ..5....1....4....5....4....3....1....2....4....0....4....3....5....1....5....4
%e A212787 ..0....0....2....3....1....0....4....5....1....1....2....1....0....5....2....1
%e A212787 ..0....4....2....4....1....3....1....5....4....4....1....3....0....3....5....5
%e A212787 ..5....0....4....0....2....0....4....1....1....5....3....3....1....2....2....4
%e A212787 ..3....0....4....4....0....0....3....4....1....5....3....4....1....5....3....4
%K A212787 nonn
%O A212787 1,1
%A A212787 _R. H. Hardin_ May 27 2012