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 A185734 Third accumulation array of the polygonal number array (A086270), by antidiagonals. 2
 1, 6, 4, 21, 25, 10, 56, 90, 65, 20, 126, 245, 240, 135, 35, 252, 560, 665, 510, 245, 56, 462, 1134, 1540, 1435, 945, 406, 84, 792, 2100, 3150, 3360, 2695, 1596, 630, 120, 1287, 3630, 5880, 6930, 6370, 4606, 2520, 930, 165, 2002, 5940, 10230 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The chain of accumulation arrays is A144257->A086270->A185732->A185733->A184734. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n,k) = C(k+3,4)*C(n+2,3)*(k*n-n+3*k+17)/20, k>=1, n>=1. T(n,k) = Sum_{j=1..n} Sum_{l=1..k} A185733(j,l), by definition. EXAMPLE Northwest corner: 1....6......21.....56....126 4....25.....90....245....560 10...65....240....665...1540 20...135...510...1435...3360 MATHEMATICA f[n_, k_]:= k*(1+k)*(2+k)*n*(1+n)*(10+2*k-n+k*n)/144; TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]  (* array A185733 *) Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten  (* A185733 *) s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *) FullSimplify[s[n, k]]  (* the formula for A185734 *) TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]]  (* array A185734 *) Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten  (* A185734 *) CROSSREFS Cf. A144112, A144257, A086270, A185732, A185733. Sequence in context: A009278 A213573 A321417 * A292696 A318209 A120462 Adjacent sequences:  A185731 A185732 A185733 * A185735 A185736 A185737 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Feb 02 2011 STATUS approved

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Last modified April 20 01:20 EDT 2021. Contains 343117 sequences. (Running on oeis4.)