A217874 Table A142978 (figurate numbers for n-dimensional cross polytope) extended by a top row.

1, 1, 0, 1, 2, 1, 1, 4, 3, 0, 1, 6, 9, 4, 1, 1, 8, 19, 16, 5, 0, 1, 10, 33, 44, 25, 6, 1, 1, 12, 51, 96, 85, 36, 7, 0, 1, 14, 73, 180, 225, 146, 49, 8, 1, 1, 16, 99, 304, 501, 456, 231, 64, 9, 0, 1, 18, 129, 476, 985, 1182, 833, 344, 81, 10, 1

Offset: 0

Author

M. F. Hasler, Oct 13 2012

Keywords

• nonn
• tabl

Comments

Looking at table A142978, it seems natural to extend it by a first row, which turns out to be 1,0,1,0,1,0,.... Indeed, these are the values obtained when the polynomial which defines each of the columns, is "extrapolated" to n=0.

Examples

			The table may be written as:
  1,_ v---- the even numbers A005843
  1,_ 0,__ v---- A058331(n) = 2*n^2 + 1.
  1,_ 2,__ 1,__ v---- 4*A006527(n) = 4n(n^2 + 2)/3.
  1,_ 4,__ 3,__ 0,__ v---- 2n^2(n^2 + 5)/3 + 1.
  1,_ 6,__ 9,__ 4,__ 1,___ v---- 2n(2n^4 + 20n^2 + 23)/15.
  1,_ 8,_ 19,_ 16,__ 5,___ 0,
  1, 10,_ 33,_ 44,_ 25,___ 6,__ 1,
  1, 12,_ 51,_ 96,_ 85,__ 36,__ 7,__ 0,
  1, 14,_ 73, 180, 225,_ 146,_ 49,__ 8,_ 1,
  1, 16,_ 99, 304, 501,_ 456, 231,_ 64,_ 9, 0,
  1, 18, 129, 476, 985, 1182, 833, 344, 81, 10, 1,...
Sequence A142978 is the table obtained by deleting the uppermost row 1,0,1,0,1,...
(One could also add a 0th column, with all zeros.)
		

Links

• J. Bodeen, S. Butler, T. Kim, X. Sun, and S. Wang, Tiling a strip with triangles, El. J. Combinat. 21 (1) (2014) P1.7.