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A185872 Accumulation array of the (odd,odd)-polka dot array A185868, by antidiagonals. 4
1, 5, 7, 16, 24, 22, 38, 59, 65, 50, 75, 120, 141, 136, 95, 131, 215, 262, 274, 245, 161, 210, 352, 440, 480, 470, 400, 252, 316, 539, 687, 770, 790, 741, 609, 372, 453, 784, 1015, 1160, 1225, 1208, 1099, 880, 525, 625, 1095, 1436, 1666, 1795, 1825, 1750, 1556, 1221, 715, 836, 1480, 1962, 2304, 2520, 2616, 2590, 2432, 2124, 1640, 946, 1090, 1947, 2605, 3090, 3420, 3605, 3647, 3540 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A144112 for the definition of accumulation array.

LINKS

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

FORMULA

T(n,k) = (k*n/6)*(4*n^2 + 6*n*k + 4*k^2 - 3*n - 9*k + 4), k>=1, n>=1.

EXAMPLE

Northwest corner:

   1,   5,  16,  38,  75

   7,  24,  59, 120, 215

  22,  54, 141, 262, 440

  50, 136, 174, 480, 770

MATHEMATICA

f[n_, k_]:=2n-1+(2n+2k-4)(2n+2k-3)/2;

TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185868 *)

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}]; (* accumulation array of {f(n, k)} *)

FullSimplify[s[n, k]] (*formula for A185872 *)

g[n_]:=Sum[f[n+1-k, k], {k, 1, n}];

Table[g[n], {n, 50}] (* A185872 *)

TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]]

CROSSREFS

Cf. A185868.

Row 1: A174723; column 1: A002412.

Sequence in context: A218623 A279175 A279875 * A186710 A276717 A318491

Adjacent sequences:  A185869 A185870 A185871 * A185873 A185874 A185875

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 05 2011

STATUS

approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)