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A026907
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Triangular array T read by rows (9-diamondization of Pascal's triangle). Step 1: t(n,k) = sum of 9 entries in diamond-shaped subarray of Pascal's triangle having vertices C(n,k), C(n+4,k+2), C(n+2,k), C(n+2,k+2). Step 2: T(n,k) = t(n,k) - t(0,0) + 1.
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14
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1, 13, 13, 28, 44, 28, 46, 90, 90, 46, 67, 154, 198, 154, 67, 91, 239, 370, 370, 239, 91, 118, 348, 627, 758, 627, 348, 118, 148, 484, 993, 1403, 1403, 993, 484, 148, 181, 650, 1495, 2414, 2824, 2414, 1495, 650, 181, 217, 849, 2163, 3927, 5256, 5256, 3927, 2163, 849, 217
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OFFSET
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0,2
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LINKS
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EXAMPLE
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Triangle starts:
1;
13, 13;
28, 44, 28;
46, 90, 90, 46;
67, 154, 198, 154, 67;
91, 239, 370, 370, 239, 91;
...
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MATHEMATICA
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t[n_, k_]:=Binomial[n + 4, k + 2 ] + Binomial[n + 3, k + 1] + Binomial[n + 3, k + 2] + Binomial[n + 2, k] + Binomial[n + 2, k + 1] + Binomial[n + 2, k + 2] + Binomial[n + 1, k] + Binomial[n + 1, k + 1] + Binomial[n, k] ; T[n_, k_]:=t[n, k] - t[0, 0] + 1; Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]] (* Indranil Ghosh, Mar 13 2017 *)
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PROG
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(PARI) alias(C, binomial);
t(n, k) = C(n+4, k+2) + C(n+3, k+1) + C(n+3, k+2) + C(n+2, k) + C(n+2, k+1) + C(n+2, k+2) + C(n+1, k) + C(n+1, k+1) + C(n, k);
T(n, k) = t(n, k)-t(0, 0)+1;
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print());
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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