A332790 Triangle read by rows: T(n,k) = 1 + 2*n + k + 5*k(n-k) for n >= 0, 0 <= k <= n.

1, 3, 4, 5, 11, 7, 7, 18, 19, 10, 9, 25, 31, 27, 13, 11, 32, 43, 44, 35, 16, 13, 39, 55, 61, 57, 43, 19, 15, 46, 67, 78, 79, 70, 51, 22, 17, 53, 79, 95, 101, 97, 83, 59, 25, 19, 60, 91, 112, 123, 124, 115, 96, 67, 28, 21, 67, 103, 129, 145, 151, 147, 133, 109, 75, 31

Offset

0,2

Links

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

Philip K. Hotchkiss, Generalized Rascal Triangles, arXiv:1907.11159 [math.HO], 2019, Figure 8 p. 3.

Formula

T(n,k) = 1 + 2*n + k + 5*k*(n-k), n >= 0, 0 <= k <= n.

Example

From Jon E. Schoenfield, Mar 14 2020: (Start)
.
  n\k|  0    1    2    3    4    5    6    7    8    9   10
  ---+-----------------------------------------------------
   0 |  1
   1 |  3    4
   2 |  5   11    7
   3 |  7   18   19   10
   4 |  9   25   31   27   13
   5 | 11   32   43   44   35   16
   6 | 13   39   55   61   57   43   19
   7 | 15   46   67   78   79   70   51   22
   8 | 17   53   79   95  101   97   83   59   25
   9 | 19   60   91  112  123  124  115   96   67   28
  10 | 21   67  103  129  145  151  147  133  109   75   31
  ...
(End)

Maple

:=proc(n, k)
   if n<0 or k<0 or k>n then
       0;
   else
       1+2*n+k+5*k*(n-k);
   end if;

Mathematica

T[n_, k_]:=1+2*n+k+5*k*(n-k); Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten

Crossrefs

Cf. A077028, A309555, A309557, A309559, A332963

Sequence in context: A261903 A133320 A225906 * A329524 A319067 A224503

Adjacent sequences: A332787 A332788 A332789 * A332791 A332792 A332793

Keyword

nonn,tabl

Author

Philip K Hotchkiss, Mar 04 2020

Status

approved