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A200154
T(n,k) = number of 0..k arrays x(0..n-1) of n elements with zero (n-1)-st difference.
14
1, 1, 2, 1, 3, 2, 1, 4, 5, 4, 1, 5, 8, 9, 2, 1, 6, 13, 22, 15, 8, 1, 7, 18, 41, 40, 39, 2, 1, 8, 25, 66, 103, 112, 45, 16, 1, 9, 32, 107, 202, 275, 182, 129, 6, 1, 10, 41, 158, 381, 730, 685, 688, 149, 32, 1, 11, 50, 219, 636, 1589, 2036, 2525, 844, 243, 2, 1, 12, 61, 304, 1033, 3000, 5153, 7488, 5221, 2090, 369, 64, 1
OFFSET
1,3
COMMENTS
Table starts
1 1 1 1 1 1 1 1 1 1 1
2 3 4 5 6 7 8 9 10 11 12
2 5 8 13 18 25 32 41 50 61 72
4 9 22 41 66 107 158 219 304 403 516
2 15 40 103 202 381 636 1033 1550 2287 3212
8 39 112 275 730 1589 3000 5181 8350 13871 21588
2 45 182 685 2036 5153 11370 23035 43284 76523 129052
16 129 688 2525 7488 18809 52166 121921 253768 484977 867086
6 149 844 5221 19262 68813 194818 514113 1171190 2531421 5019770
32 243 2090 13897 62772 256859 841122 2347671 6169890 14503751 31169760
T(n,k) is the number of integer lattice points in k*C(n) where C(n) is a certain polytope with vertices having rational entries (the intersection of [0,1]^n with a hyperplane). Thus row n is an Ehrhart quasi-polynomial of degree n-1. - Robert Israel, Dec 12 2019
LINKS
EXAMPLE
Some solutions for n=7, k=6:
5 6 5 3 6 0 0 5 4 1 2 2 0 2 1 2
3 1 5 1 6 5 4 0 2 5 2 0 2 0 4 0
3 3 6 5 6 1 6 2 0 1 1 4 3 4 6 2
3 2 3 6 5 1 3 6 0 2 1 6 3 3 6 3
2 0 2 5 5 3 2 6 1 6 2 5 3 1 5 2
1 1 6 5 6 2 6 1 2 6 3 3 4 3 4 1
4 1 1 3 1 2 0 1 5 0 3 1 6 1 2 4
PROG
(PARI) pad(d, n) = while(#d != n, d = concat([0], d)); d;
mydigits(i, n) = if (n<2, vector(i), digits(i, n));
bedt(n) = {for(i=2, #n=n, n=vecextract(n, "^1")-vecextract(n, "^-1")); n[1]; }
T(n, k) = {k++; my(nbok = 0); for (i=0, k^n-1, d = pad(mydigits(i, k), n); if (bedt(d) == 0, nbok++); ); nbok; } \\ Michel Marcus, Apr 08 2017
CROSSREFS
Row 3 is A000982(n+1).
Cf. A187202 (for 3rd PARI function).
Sequence in context: A104741 A167237 A277813 * A208825 A344391 A089353
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 13 2011
STATUS
approved