cp's OEIS Frontend

A200154 T(n,k) = number of 0..k arrays x(0..n-1) of n elements with zero (n-1)-st difference.

%I A200154 #28 Dec 13 2019 05:59:02
%S A200154 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,
%T A200154 25,66,103,112,45,16,1,9,32,107,202,275,182,129,6,1,10,41,158,381,730,
%U A200154 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
%N A200154 T(n,k) = number of 0..k arrays x(0..n-1) of n elements with zero (n-1)-st difference.
%C A200154 Table starts
%C A200154    1   1    1     1     1      1      1       1       1        1        1
%C A200154    2   3    4     5     6      7      8       9      10       11       12
%C A200154    2   5    8    13    18     25     32      41      50       61       72
%C A200154    4   9   22    41    66    107    158     219     304      403      516
%C A200154    2  15   40   103   202    381    636    1033    1550     2287     3212
%C A200154    8  39  112   275   730   1589   3000    5181    8350    13871    21588
%C A200154    2  45  182   685  2036   5153  11370   23035   43284    76523   129052
%C A200154   16 129  688  2525  7488  18809  52166  121921  253768   484977   867086
%C A200154    6 149  844  5221 19262  68813 194818  514113 1171190  2531421  5019770
%C A200154   32 243 2090 13897 62772 256859 841122 2347671 6169890 14503751 31169760
%C A200154 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
%H A200154 R. H. Hardin, <a href="/A200154/b200154.txt">Table of n, a(n) for n = 1..321</a>
%e A200154 Some solutions for n=7, k=6:
%e A200154   5  6  5  3  6  0  0  5  4  1  2  2  0  2  1  2
%e A200154   3  1  5  1  6  5  4  0  2  5  2  0  2  0  4  0
%e A200154   3  3  6  5  6  1  6  2  0  1  1  4  3  4  6  2
%e A200154   3  2  3  6  5  1  3  6  0  2  1  6  3  3  6  3
%e A200154   2  0  2  5  5  3  2  6  1  6  2  5  3  1  5  2
%e A200154   1  1  6  5  6  2  6  1  2  6  3  3  4  3  4  1
%e A200154   4  1  1  3  1  2  0  1  5  0  3  1  6  1  2  4
%o A200154 (PARI) pad(d, n) = while(#d != n, d = concat([0], d)); d;
%o A200154 mydigits(i,n) = if (n<2, vector(i), digits(i,n));
%o A200154 bedt(n) = {for(i=2, #n=n, n=vecextract(n, "^1")-vecextract(n, "^-1")); n[1];}
%o A200154 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
%Y A200154 Row 3 is A000982(n+1).
%Y A200154 Cf. A187202 (for 3rd PARI function).
%K A200154 nonn,tabl
%O A200154 1,3
%A A200154 _R. H. Hardin_, Nov 13 2011