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A212782 T(n,k)=Half the number of 0..k arrays of length n+2 with second differences nonzero.

%I A212782 #6 Jul 22 2025 22:57:28
%S A212782 3,11,5,28,27,8,56,99,66,13,99,252,350,162,21,159,546,1134,1238,397,
%T A212782 34,240,1034,3010,5104,4379,973,55,344,1803,6724,16594,22972,15490,
%U A212782 2385,89,475,2925,13544,43727,91482,103391,54793,5846,144,635,4517,24870,101743
%N A212782 T(n,k)=Half the number of 0..k arrays of length n+2 with second differences nonzero.
%C A212782 Table starts
%C A212782 ...3....11......28.......56........99........159.........240.........344
%C A212782 ...5....27......99......252.......546.......1034........1803........2925
%C A212782 ...8....66.....350.....1134......3010.......6724.......13544.......24870
%C A212782 ..13...162....1238.....5104.....16594......43727......101743......211461
%C A212782 ..21...397....4379....22972.....91482.....284360......764297.....1797975
%C A212782 ..34...973...15490...103391....504337....1849215.....5741427....15287517
%C A212782 ..55..2385...54793...465336...2780392...12025596....43129809...129984123
%C A212782 ..89..5846..193821..2094360..15328203...78203437...323992699..1105207105
%C A212782 .144.14329..685609..9426184..84503842..508563345..2433844978..9397168738
%C A212782 .233.35122.2425226.42424863.465866699.3307229006.18283132290.79900662826
%H A212782 R. H. Hardin, <a href="/A212782/b212782.txt">Table of n, a(n) for n = 1..9999</a>
%e A212782 Some solutions for n=5 k=4
%e A212782 ..2....2....2....1....2....4....1....3....3....4....3....2....1....1....0....4
%e A212782 ..0....2....2....1....2....2....4....4....1....1....4....4....3....3....3....3
%e A212782 ..3....3....0....2....1....2....2....0....0....3....2....1....0....3....2....3
%e A212782 ..2....3....2....4....3....4....3....2....4....3....3....3....2....2....3....4
%e A212782 ..3....1....2....4....4....1....0....0....3....1....2....4....1....0....0....1
%e A212782 ..2....3....0....2....3....1....4....3....3....1....0....3....3....1....1....1
%e A212782 ..4....3....4....2....1....2....0....0....1....0....2....1....3....1....1....4
%Y A212782 Column 1 is A000045(n+3)
%Y A212782 Row 1 is A182260(n+1)
%K A212782 nonn,tabl
%O A212782 1,1
%A A212782 _R. H. Hardin_ May 27 2012