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T(n,k)=Half the number of 0..k arrays of length n+2 with second differences nonzero
13

%I #4 May 27 2012 06:56:00

%S 3,11,5,28,27,8,56,99,66,13,99,252,350,162,21,159,546,1134,1238,397,

%T 34,240,1034,3010,5104,4379,973,55,344,1803,6724,16594,22972,15490,

%U 2385,89,475,2925,13544,43727,91482,103391,54793,5846,144,635,4517,24870,101743

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

%C Table starts

%C ...3....11......28.......56........99........159.........240.........344

%C ...5....27......99......252.......546.......1034........1803........2925

%C ...8....66.....350.....1134......3010.......6724.......13544.......24870

%C ..13...162....1238.....5104.....16594......43727......101743......211461

%C ..21...397....4379....22972.....91482.....284360......764297.....1797975

%C ..34...973...15490...103391....504337....1849215.....5741427....15287517

%C ..55..2385...54793...465336...2780392...12025596....43129809...129984123

%C ..89..5846..193821..2094360..15328203...78203437...323992699..1105207105

%C .144.14329..685609..9426184..84503842..508563345..2433844978..9397168738

%C .233.35122.2425226.42424863.465866699.3307229006.18283132290.79900662826

%H R. H. Hardin, <a href="/A212782/b212782.txt">Table of n, a(n) for n = 1..9999</a>

%e Some solutions for n=5 k=4

%e ..2....2....2....1....2....4....1....3....3....4....3....2....1....1....0....4

%e ..0....2....2....1....2....2....4....4....1....1....4....4....3....3....3....3

%e ..3....3....0....2....1....2....2....0....0....3....2....1....0....3....2....3

%e ..2....3....2....4....3....4....3....2....4....3....3....3....2....2....3....4

%e ..3....1....2....4....4....1....0....0....3....1....2....4....1....0....0....1

%e ..2....3....0....2....3....1....4....3....3....1....0....3....3....1....1....1

%e ..4....3....4....2....1....2....0....0....1....0....2....1....3....1....1....4

%Y Column 1 is A000045(n+3)

%Y Row 1 is A182260(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ May 27 2012