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A185912 Accumulation array of A185910; by antidiagonals. 4
1, 3, 5, 6, 12, 14, 10, 21, 31, 30, 15, 32, 51, 64, 55, 21, 45, 74, 102, 115, 91, 28, 60, 100, 144, 180, 188, 140, 36, 77, 129, 190, 250, 291, 287, 204, 45, 96, 161, 240, 325, 400, 441, 416, 285, 55, 117, 196, 294, 405, 515, 602, 636, 579, 385, 66, 140, 234, 352, 490, 636, 770, 864, 882, 780, 506, 78, 165, 275, 414, 580, 763, 945, 1100, 1194, 1185, 1023, 650, 91, 192, 319, 480, 675, 896, 1127, 1344, 1515, 1600, 1551, 1312, 819, 105 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A member of the accumulation chain ... < A185910 < A185911 < A185912 < A185913 < ...

(See A144112 for definitions of weight array and accumulation array.)

LINKS

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

FORMULA

T(n,k) = (k*n/6)*(2*n^2 + 3*n + 3*k - 2), k >= 1, n >= 1.

EXAMPLE

Northwest corner:

   1,   3,   6,  10,  15

   5,  12,  21,  32,  45

  14,  31,  51,  74, 100

  30,  64, 102, 144, 190

MATHEMATICA

f[n_, 0] := 0; f[0, k_] := 0;

f[n_, k_] := n^2 + k - 1;

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

FullSimplify[s[n, k]]  (*formula for A185812*)

Table[s[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten

T[n_, k_] := (k*n/6)*(2*n^2 + 3*n + 3*k - 2) ; Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 22 2017 *)

CROSSREFS

Cf. A144112, A185910, A185913.

Row 1 to 2: A000217, A028347.

Column 1 to 3: A000330, A037237, 3*A145066.

Sequence in context: A268495 A127577 A280590 * A100712 A086187 A088082

Adjacent sequences:  A185909 A185910 A185911 * A185913 A185914 A185915

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 06 2011

STATUS

approved

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Last modified September 19 19:41 EDT 2021. Contains 347564 sequences. (Running on oeis4.)