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 A181634 Irregular triangle T(n,k) where row n contains all pairs [a,b] of the compositions n=a+b into nonnegative pairs where a == b (mod 3). 1
 1, 1, 3, 0, 0, 3, 2, 2, 4, 1, 1, 4, 6, 0, 3, 3, 0, 6, 5, 2, 2, 5, 7, 1, 4, 4, 1, 7, 9, 0, 6, 3, 3, 6, 0, 9, 8, 2, 5, 5, 2, 8, 10, 1, 7, 4, 4, 7, 1, 10, 12, 0, 9, 3, 6, 6, 3, 9, 0, 12, 11, 2, 8, 5, 5, 8, 2, 11, 13, 1, 10, 4, 7, 7, 4, 10, 1, 13, 15, 0, 12, 3, 9, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Row lengths are 2*A008611(n). Row sums are n*A008611(n).- R. J. Mathar, May 13 2016 LINKS Table of n, a(n) for n=2..86. EXAMPLE 1, 1; 3, 0, 0, 3; 2, 2; 4, 1, 1, 4; 6, 0, 3, 3, 0, 6; 5, 2, 2, 5; 7, 1, 4, 4, 1, 7; 9, 0, 6, 3, 3, 6, 0, 9; 8, 2, 5, 5, 2, 8; 10, 1, 7, 4, 4, 7, 1, 10; 12, 0, 9, 3, 6, 6, 3, 9, 0, 12; 11, 2, 8, 5, 5, 8, 2, 11; 13, 1, 10, 4, 7, 7, 4, 10, 1, 13; 15, 0, 12, 3, 9, 6, 6, 9, 3, 12, 0, 15; 14, 2, 11, 5, 8, 8, 5, 11, 2, 14; MAPLE A181634_row := proc(n) local L, a, b; L := [] ; for a from n to 0 by -1 do b := n-a ; if modp(a, 3) = modp(b, 3) then L := [op(L), a, b] ; end if; end do: L ; end proc: for n from 2 to 18 do print(op(A181634_row(n))) ; end do: # R. J. Mathar, May 13 2016 MATHEMATICA If[First@ # == Last@ # &@ Take[#, 2], Join[Reverse@ Drop[#, 2], #], Join[Reverse@ #, #]] & /@ Function[n, Flatten@ Select[Transpose@ {n - #, #}, Mod[First@ #, 3] == Mod[Last@ #, 3] &] &@ Range[Ceiling[n/2], n]] /@ Range[2, 16] // Flatten (* Michael De Vlieger, May 13 2016 *) CROSSREFS Sequence in context: A359967 A284281 A075874 * A230652 A230661 A178952 Adjacent sequences: A181631 A181632 A181633 * A181635 A181636 A181637 KEYWORD nonn,easy,tabf,less AUTHOR Florentin Smarandache (smarand(AT)unm.edu), Nov 03 2010 EXTENSIONS Edited by R. J. Mathar, May 13 2016 STATUS approved

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Last modified May 29 04:26 EDT 2024. Contains 372921 sequences. (Running on oeis4.)