# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a185915 Showing 1-1 of 1 %I A185915 #12 Jul 23 2017 03:54:09 %S A185915 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 A185915 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 A185915 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 A185915 Accumulation array of A185914, by antidiagonals. %C A185915 A member of the accumulation chain ... < A185916 < A185914 < A185915 < ... %C A185915 (See A144112 for definitions of weight array and accumulation array.) %H A185915 G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened %F A185915 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 A185915 Northwest corner: %e A185915 1....3....6....10....15....21....28 %e A185915 1....4....9....16....25....36....49 %e A185915 1....4....10...19....31....46....64 %e A185915 1....4....10...20....34....52....74 %e A185915 1....4....10...20....35....55....80 %e A185915 1....4....10...20....35....56....83 %e A185915 row 1: A000217 (triangular numbers) %e A185915 row 2: A000290 (squares) %e A185915 row 3: A005448 (centered triangular numbers) %e A185915 row 4: A005893 %e A185915 row 5: A062985 %e A185915 Limit of rows: A000292 (tetrahedral numbers) %t A185915 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 A185915 Cf. A144112, A185914, A185916. %K A185915 nonn,tabl %O A185915 1,2 %A A185915 _Clark Kimberling_, Feb 06 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE