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A027170 Triangular array T read by rows (4-diamondization of Pascal's triangle). Step 1: t(n,k) = C(n+2,k+1) + C(n+1,k) + C(n+1,k+1) + C(n,k). Step 2: T(n,k) = t(n,k) - t(0,0) + 1. Domain: 0 <= k <= n, n >= 0.

%I A027170 #30 Apr 18 2020 09:21:46
%S A027170 1,3,3,5,10,5,7,19,19,7,9,30,42,30,9,11,43,76,76,43,11,13,58,123,156,
%T A027170 123,58,13,15,75,185,283,283,185,75,15,17,94,264,472,570,472,264,94,
%U A027170 17,19,115,362,740,1046,1046,740,362,115,19,21,138,481,1106,1790,2096,1790,1106,481,138,21
%N A027170 Triangular array T read by rows (4-diamondization of Pascal's triangle). Step 1: t(n,k) = C(n+2,k+1) + C(n+1,k) + C(n+1,k+1) + C(n,k). Step 2: T(n,k) = t(n,k) - t(0,0) + 1. Domain: 0 <= k <= n, n >= 0.
%H A027170 Indranil Ghosh, <a href="/A027170/b027170.txt">Rows of n = 0..125 of triangle, flattened</a>
%e A027170 Triangle starts:
%e A027170    1;
%e A027170    3,  3;
%e A027170    5, 10,  5;
%e A027170    7, 19, 19,  7;
%e A027170    9, 30, 42, 30,  9;
%e A027170   11, 43, 76, 76, 43, 11;
%e A027170   ...
%t A027170 t[n_, k_]:= Binomial[n + 2, k + 1] + 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, 10},{k, 0, n}]] (* _Indranil Ghosh_, Mar 13 2017 *)
%o A027170 (PARI) alias(C, binomial);
%o A027170 t(n,k) = C(n+2,k+1)+C(n+1,k)+C(n+1,k+1)+C(n,k);
%o A027170 T(n,k) = t(n,k)-t(0,0)+1;
%o A027170 tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print());
%o A027170 \\ _Michel Marcus_, Mar 13 2017
%Y A027170 Cf. A007318, A026907.
%K A027170 nonn,tabl
%O A027170 0,2
%A A027170 _Clark Kimberling_