

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 Stirlinglike 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 Stirlingtype 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 Stirlingtype sequences, Europ. J. Combin., 43, 2015, 5567.


FORMULA

T(n,k) = [k<=n]*floor((k+2)/2)*(nk+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(n1).


MATHEMATICA

T[n_, k_] := If[EvenQ[k], (k+2)(2nk+2)/4, (k+1)(2nk+3)/4];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* JeanFrançois 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



