Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Apr 18 2020 09:21:36
%S 1,13,13,28,44,28,46,90,90,46,67,154,198,154,67,91,239,370,370,239,91,
%T 118,348,627,758,627,348,118,148,484,993,1403,1403,993,484,148,181,
%U 650,1495,2414,2824,2414,1495,650,181,217,849,2163,3927,5256,5256,3927,2163,849,217
%N 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.
%H Indranil Ghosh, <a href="/A026907/b026907.txt">Rows 0..125, flattened</a>
%e Triangle starts:
%e 1;
%e 13, 13;
%e 28, 44, 28;
%e 46, 90, 90, 46;
%e 67, 154, 198, 154, 67;
%e 91, 239, 370, 370, 239, 91;
%e ...
%t 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 *)
%o (PARI) alias(C, binomial);
%o 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);
%o T(n,k) = t(n,k)-t(0,0)+1;
%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print());
%o \\ _Michel Marcus_, Mar 13 2017
%Y Cf. A007318, A027170.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_