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 A217874 Table A142978 (figurate numbers for n-dimensional 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified February 6 18:02 EST 2023. Contains 360111 sequences. (Running on oeis4.)