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
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
KEYWORD
nonn,tabl
AUTHOR
M. F. Hasler, Oct 13 2012
STATUS
approved