login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A185780 Array T(n,k) = k*(n*k-n+1), by antidiagonals. 4
1, 4, 1, 9, 6, 1, 16, 15, 8, 1, 25, 28, 21, 10, 1, 36, 45, 40, 27, 12, 1, 49, 66, 65, 52, 33, 14, 1, 64, 91, 96, 85, 64, 39, 16, 1, 81, 120, 133, 126, 105, 76, 45, 18, 1, 100, 153, 176, 175, 156, 125, 88, 51, 20, 1, 121, 190, 225, 232, 217, 186, 145, 100, 57, 22, 1, 144, 231, 280, 297, 288, 259, 216, 165, 112, 63, 24, 1, 169, 276, 341, 370, 369, 344, 301, 246, 185, 124, 69, 26, 1, 196, 325, 408, 451, 460, 441, 400, 343, 276, 205, 136, 75, 28, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A185780 is the accumulation array of A185781, the weight array of A185782, and second weight array of A185783.  See A144112 for definitions of accumulation array and weight array.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

T(n,k) = k*(n*k - n + 1), k>=1, n>=1.

EXAMPLE

Northwest corner:

1....4....9....16....25....36

1....6....15...28....45....66

1....8....21...40....65....96

1....10...27...52....85....126

MATHEMATICA

(* This code yields arrays A185780, A185781, and A185782. *)

f[n_, 0]:=0; f[0, k_]:=0;  (* Used to make weight array A185782 *)

f[n_, k_]:=k(n*k-n+1);

TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185780 *)

Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* acc array of {f(n, k)} *)

FullSimplify[s[n, k]]

TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]]  (* A185781 *)

Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

w[m_, n_]:=f[m, n]+f[m-1, n-1]-f[m, n-1]-f[m-1, n]/; Or[m>0, n>0];

TableForm[Table[w[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185782 *)

Table[w[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten (* seq A185782 *)

CROSSREFS

Cf. A144112, A185781, A185782, A185783.

Sequence in context: A065489 A197258 A211783 * A051672 A156308 A325004

Adjacent sequences:  A185777 A185778 A185779 * A185781 A185782 A185783

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 03 2011

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)