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A080251 Paired decomposition of tetrahedral numbers A000292 arranged as number triangle. 2
1, 2, 2, 3, 3, 4, 4, 4, 6, 6, 5, 5, 8, 8, 9, 6, 6, 10, 10, 12, 12, 7, 7, 12, 12, 15, 15, 16, 8, 8, 14, 14, 18, 18, 20, 20, 9, 9, 16, 16, 21, 21, 24, 24, 25, 10, 10, 18, 18, 24, 24, 28, 28, 30, 30, 11, 11, 20, 20, 27, 27, 32, 32, 35, 35, 36 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used in construction of Stirling-like number triangle A080416.

LINKS

Table of n, a(n) for n=0..65.

R. B. Corcino, K. J. M. Gonzales, M. J. C. Loquias and E. L. Tan, Dually weighted Stirling-type sequences, arXiv preprint arXiv:1302.4694 [math.CO], 2013.

R. B. Corcino, K. J. M. Gonzales, M. J. C. Loquias and E. L. Tan, Dually weighted Stirling-type sequences, Europ. J. Combin., 43, 2015, 55-67.

FORMULA

T(n,k) = [k<=n]*floor((k+2)/2)*(n-k+floor((k+3)/2)). - Paul Barry, Jun 14 2010

Also generated by the product of pairs of integers 0 <= r1,r2 <= n whose sum is n+2.

Viewed as a square array: T(n,2*k) = k*(k+n); T(n,2*k+1) = (k+1)*(k+n). - Luc Rousseau, Dec 11 2017

EXAMPLE

Rows are

  1;

  2,2;

  3,3,4;

  4,4,6,6;

  5,5,8,8,9;

  ...

Row sums are 1, 4, 10, 20, ... or C(n+3,3) = A000292(n-1).

MATHEMATICA

T[n_, k_] := If[EvenQ[k], (k+2)(2n-k+2)/4, (k+1)(2n-k+3)/4];

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Dec 13 2018 *)

CROSSREFS

Sequence in context: A103358 A063084 A127079 * A220032 A219773 A187446

Adjacent sequences:  A080248 A080249 A080250 * A080252 A080253 A080254

KEYWORD

nonn,tabl

AUTHOR

Paul Barry, Feb 17 2003

EXTENSIONS

Edited by Ken Joffaniel M Gonzales, Jul 04 2010

STATUS

approved

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Last modified May 21 08:44 EDT 2022. Contains 353908 sequences. (Running on oeis4.)