A132108 - OEIS

%I #17 Sep 08 2022 08:45:31

%S 1,2,1,3,3,1,4,5,4,1,5,7,8,5,1,6,9,13,12,6,1,7,11,19,23,17,7,1,8,13,

%T 26,39,38,23,8,1,9,15,34,61,74,59,30,9,1,10,17,43,90,131,130,87,38,10,

%U 1

%N Triangle T(n,k) = binomial(n,k)+n-k read by rows.

%H Harvey P. Dale, <a href="/A132108/b132108.txt">Table of n, a(n) for n = 0..5000</a>

%F T(n,k) = A007318(n,k) + A002024(n,k) - A002260(n,k).

%e First few rows of the triangle are:

%e 1;

%e 2, 1;

%e 3, 3, 1;

%e 4, 5, 4, 1;

%e 5, 7, 8, 5, 1;

%e 6, 9, 13, 12, 6, 1;

%e 7, 11, 19, 23, 17, 7, 1;

%e ...

%t Table[Binomial[n,k]+n-k,{n,0,10},{k,0,n}]//Flatten (* _Harvey P. Dale_, Mar 08 2018 *)

%o (Magma) /* As triangle: */ [[Binomial(n,k)+n-k: k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, May 23 2016

%Y Cf. A007318, A002024, A002260, A132109 (row sums).

%K nonn,easy,tabl

%O 0,2

%A _Gary W. Adamson_, Aug 09 2007