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

0,5

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.

Links

Table of n, a(n) for n=0..65.

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

Example

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.)

Crossrefs

Sequence in context: A335941 A157143 A112096 * A323182 A229118 A320796

Adjacent sequences: A217871 A217872 A217873 * A217875 A217876 A217877

Keyword

nonn,tabl

Author

M. F. Hasler, Oct 13 2012

Status

approved