The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309559 Triangle read by rows: T(n,k) = 1 + n + k^2/2 - k/2 + k*(n-k), n >= 0, 0 <= k <= n. 4
 1, 2, 2, 3, 4, 4, 4, 6, 7, 7, 5, 8, 10, 11, 11, 6, 10, 13, 15, 16, 16, 7, 12, 16, 19, 21, 22, 22, 8, 14, 19, 23, 26, 28, 29, 29, 9, 16, 22, 27, 31, 34, 36, 37, 37, 10, 18, 25, 31, 36, 40, 43, 45, 46, 46, 11, 20, 28, 35, 41, 46, 50, 53, 55, 56, 56, 12, 22, 31, 39, 46, 52, 57, 61, 64, 66, 67, 67, 13, 24, 34, 43, 51, 58, 64, 69, 73, 76, 78, 79, 79 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The rascal triangle (A077028) can be generated by  the rule South = (East*West+1)/North or South = East+West+1-North; this number triangle can also be generated by South = East+West+1-North, but there not by an equation of the form South = (East*West+d)/North. LINKS Philip K Hotchkiss, Generalized Rascal Triangles, arXiv:1907.11159 [math.HO], 2019. FORMULA G.f.: (-1+(3-2*x)*y+(-1+x)*y^2)/((-1+x)^2*(-1+y)^3). - Stefano Spezia, Sep 08 2019 EXAMPLE For row n=3: T(3,0)=4, T(3,1)=6, T(3,2)=6, T(3,3)=7. Triangle T begins:                   1                 2   2               3   4   4             4   6   7   7           5   8  10  11  11         6  10  13  15  16  16       7  12  16  19  21  22  22     8  14  19  23  26  28  29  29   9  16  22  27  31  34  36  37  37                  ... MAPLE T := proc(n, k)    if n<0 or k<0 or k>n then        0;    else        1+n+(1/2)*k^2-(1/2)k +k*(n-k);    end if; MATHEMATICA T[n_, k_]:=1+n+(1/2)*k^2-(1/2)k +k*(n-k); Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten f[n_] := Table[SeriesCoefficient[(-1+(3-2*x)*y+(-1+x)*y^2)/((-1+x)^2*(-1+y)^3), {x, 0, i}, {y, 0, j}], {i, n, n}, {j, 0, n}]; Flatten[Array[f, 13, 0]] (* Stefano Spezia, Sep 08 2019 *) CROSSREFS Cf. A077028, A309555, A309557. Sequence in context: A070172 A273353 A259197 * A130128 A210556 A208914 Adjacent sequences:  A309556 A309557 A309558 * A309560 A309561 A309562 KEYWORD nonn,tabl AUTHOR Philip K Hotchkiss, Aug 07 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 13 17:54 EDT 2020. Contains 335689 sequences. (Running on oeis4.)