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 A104566 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2; ...] and R = [1; 1,1; 1,1,1; 1,1,1,1; ...]. 2
 1, 3, 2, 4, 3, 1, 6, 5, 3, 2, 7, 6, 4, 3, 1, 9, 8, 6, 5, 3, 2, 10, 9, 7, 6, 4, 3, 1, 12, 11, 9, 8, 6, 5, 3, 2, 13, 12, 10, 9, 7, 6, 4, 3, 1, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1, 18, 17, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2, 19, 18, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA For 1 <= j <= i: T(i,j) = 3(i-j+1)/2 if i and j are of opposite parity; T(i,j) = 3(i-j)/2 + 1 if both i and j are odd; T(i,j) = 3(i-j)/2 + 2 if both i and j are even. - Emeric Deutsch, Mar 24 2005 EXAMPLE The first few rows are   1;   3, 2;   4, 3, 1;   6, 5, 3, 2;   ... MAPLE T:=proc(i, j) if j>i then 0 elif i mod 2 = 1 and j mod 2 = 1 then 3*(i-j)/2+1 elif i mod 2 = 0 and j mod 2 = 0 then 3*(i-j)/2+2 elif i+j mod 2 = 1 then 3*(i-j+1)/2 else fi end: for i from 1 to 14 do seq(T(i, j), j=1..i) od; # yields sequence in triangular form # Emeric Deutsch, Mar 24 2005 CROSSREFS Row sums yield A001082. Columns 1, 3, 5, ... (starting at the diagonal entry) yield A032766. Columns 2, 4, 6, ... (starting at the diagonal entry) yield A045506. Row sums = 1, 5, 8, 16, 21, ... (generalized octagonal numbers, A001082). A006578(2n-1) = A001082(2n). Sequence in context: A106288 A013633 A016559 * A143156 A227471 A101403 Adjacent sequences:  A104563 A104564 A104565 * A104567 A104568 A104569 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Mar 15 2005 EXTENSIONS More terms from Emeric Deutsch, Mar 24 2005 STATUS approved

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Last modified February 27 06:36 EST 2020. Contains 332299 sequences. (Running on oeis4.)