id:A056558 - OEIS Search Results

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Third tetrahedral co-ordinate, i.e. tetrahedron with T(t,n,k)=k; succession of growing finite triangles with increasing values towards bottom right.

+0
14

0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5 (list; graph; listen)

	OFFSET	`0,10`
	COMMENT	`If {(X,Y,Z)} are triples of nonnegative integers with X>=Y>=Z ordered by X, Y and Z, then X=A056556(n), Y=A056557(n) and Z=A056558(n)` `Contribution from Peter Luschny (peter(AT)luschny.de), Jul 14 2009: (Start)` `This is a 'Matryoshka doll' sequence with alpha=0 (cf. A000292 and A000178),` `seq(seq(seq(i,i=alpha..k),k=alpha..n),n=alpha..6). (End)`
	FORMULA	`a(n) =n-A056556(n)(A056556(n)+1)(A056556(n)+2)/6-A056557(n)*(A056557(n)+1)/2 =n-A000292(A056556(n)-1)-A000217(A056557(n)) =A056557(n)-A056560(n)` `a(n+1) = A056556(n)==a(n) ? 0 : A056557(n)==a(n) ? 0 : a(n)+1 - Graeme McRae (g_m(AT)mcraefamily.com), Jan 09 2007`
	EXAMPLE	`First triangle: [0]; second triangle: [0; 0 1]; third triangle: [0; 0 1; 0 1 2]; ...`
	CROSSREFS	`Together with A056559 and A056560 might enable reading "by antidiagonals" of cube arrays as 3-dimensional analogue of A002262 and A025581 with square arrays. Also cf. A000292, A056556, A056557.` `Sequence in context: A035168 A119241 A001878 this_sequence A091979 A029430 A092303` `Adjacent sequences: A056555 A056556 A056557 this_sequence A056559 A056560 A056561`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Jun 26 2000`

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Last modified December 6 13:45 EST 2009. Contains 170429 sequences.

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