A185909 - OEIS

%I #12 Jul 22 2017 09:15:03

%S 1,2,3,3,7,6,4,11,14,10,5,15,23,23,15,6,19,32,38,34,21,7,23,41,54,56,

%T 47,28,8,27,50,70,80,77,62,36,9,31,59,86,105,110,101,79,45,10,35,68,

%U 102,130,145,144,128,98,55,11,39,77,118,155,181,190,182,158,119,66,12,43,86,134,180,217,238,240,224,191,142,78,13,47,95,150,205,253,287,301,295,270,227,167,91,14,51,104,166,230,289,336,364,370,355,320,266,194,105,15,55,113,182,255

%N Accumulation array of A185908, by antidiagonals.

%C A member of the accumulation chain ... < A185907 < A185908 < A185909 < ...

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

%H G. C. Greubel, <a href="/A185909/b185909.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%e Northwest corner:

%e    1,  2,  3,  4,  5

%e    3,  7, 11, 15, 19

%e    6, 14, 23, 32, 41

%e   10, 23, 38, 54, 70

%t f[n_, 0] := 0; f[0, k_] := 0; (*needed for the weight array*)

%t f[n_, k_] := Min[n, k] + n - 1;

%t s[n_, k_] := Sum[f[i, j], {i, 1, n}, {j, 1, k}];

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

%Y Cf. A144112, A185907, A185908.

%Y diag (1,7,...): A004068.

%Y diag (2,11,...): A033994.

%Y diag (3,14,...): A162147.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 06 2011