

A217874


Table A142978 (figurate numbers for ndimensional cross polytope) extended by a top row.


0



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
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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: A157125 A157143 A112096 * A229118 A320796 A026725
Adjacent sequences: A217871 A217872 A217873 * A217875 A217876 A217877


KEYWORD

nonn,tabl


AUTHOR

M. F. Hasler, Oct 13 2012


STATUS

approved



