A185915 - OEIS

%I #12 Jul 23 2017 03:54:09

%S 1,3,1,6,4,1,10,9,4,1,15,16,10,4,1,21,25,19,10,4,1,28,36,31,20,10,4,1,

%T 36,49,46,34,20,10,4,1,45,64,64,52,35,20,10,4,1,55,81,85,74,55,35,20,

%U 10,4,1,66,100,109,100,80,56,35,20,10,4,1,78,121,136,130,110,83,56,35,20,10,4,1,91,144,166,164,145,116,84,56,35,20,10,4,1,105,169,199,202,185,155,119,84,56,35,20,10,4,1

%N Accumulation array of A185914, by antidiagonals.

%C A member of the accumulation chain ... < A185916 < A185914 < A185915 < ...

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

%H G. C. Greubel, <a href="/A185915/b185915.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F T(n,k) = C(k+2,3) if k<=n; T(n,k) = k*(k+2-n)/2 if k>n; k>=1, n>=1.

%e Northwest corner:

%e 1....3....6....10....15....21....28

%e 1....4....9....16....25....36....49

%e 1....4....10...19....31....46....64

%e 1....4....10...20....34....52....74

%e 1....4....10...20....35....55....80

%e 1....4....10...20....35....56....83

%e row 1: A000217 (triangular numbers)

%e row 2: A000290 (squares)

%e row 3: A005448 (centered triangular numbers)

%e row 4: A005893

%e row 5: A062985

%e Limit of rows: A000292 (tetrahedral numbers)

%t f[n_, 0] := 0; f[0, k_] := 0; f[n_, k_] := k - n + 1; f[n_, k_] := 0 /; k < n; s[n_, k_] := Sum[f[i, j], {i, 1, n}, {j, 1, k}]; Table[s[n - k + 1, k], {n, 50}, {k, n, 1, -1}] // Flatten

%Y Cf. A144112, A185914, A185916.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 06 2011