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A028324 Elements to the right of the central elements of the 5-Pascal triangle A028313 that are not 1.

%I A028324 #13 Jul 02 2025 16:01:56
%S A028324 6,7,19,8,27,9,65,36,10,101,46,11,231,147,57,12,378,204,69,13,840,582,
%T A028324 273,82,14,1422,855,355,96,15,3102,2277,1210,451,111,16,5379,3487,
%U A028324 1661,562,127,17,11583,8866,5148,2223,689,144,18,20449,14014,7371,2912,833
%N A028324 Elements to the right of the central elements of the 5-Pascal triangle A028313 that are not 1.
%H A028324 G. C. Greubel, <a href="/A028324/b028324.txt">Rows n = 0..100 of the irregular triangle, flattened</a>
%F A028324 T(n, k) = binomial(n+3, k + 2 + floor((n+1)/2)) + 3*binomial(n+1, k + 1 + floor((n+1)/2)), for 0 <= k <= floor(n/2), n >= 0. - _G. C. Greubel_, Jan 06 2024
%e A028324 This sequence represents the following portion of A028313(n,k), with x being the elements of A028313(2*n,n):
%e A028324   x;
%e A028324   .,  .;
%e A028324   .,  x,  .;
%e A028324   .,  .,  6,   .;
%e A028324   .,  .,  x,   7,   .;
%e A028324   .,  .,  .,  19,   8,   .;
%e A028324   .,  .,  .,   x,  27,   9,   .;
%e A028324   .,  .,  .,   .,  65,  36,  10,   .;
%e A028324   .,  .,  .,   .,   x, 101,  46,  11,  .;
%e A028324   .,  .,  .,   .,   ., 231, 147,  57, 12,  .;
%e A028324   .,  .,  .,   .,   .,   x, 378, 204, 69, 13,  .;
%e A028324 As an irregular triangle this sequence begins as:
%e A028324       6;
%e A028324       7;
%e A028324      19,    8;
%e A028324      27,    9;
%e A028324      65,   36,   10;
%e A028324     101,   46,   11;
%e A028324     231,  147,   57,   12;
%e A028324     378,  204,   69,   13;
%e A028324     840,  582,  273,   82,  14;
%e A028324    1422,  855,  355,   96,  15;
%e A028324    3102, 2277, 1210,  451, 111,  16;
%e A028324    5379, 3487, 1661,  562, 127,  17;
%e A028324   11583, 8866, 5148, 2223, 689, 144, 18;
%t A028324 T[n_, k_]:= Binomial[n+3, k+2+Floor[(n+1)/2]] + 3*Binomial[n+1, k+1 + Floor[(n+1)/2]];
%t A028324 Table[T[n,k], {n,0,16}, {k,0,Floor[n/2]}]//Flatten (* _G. C. Greubel_, Jan 06 2024 *)
%o A028324 (Magma)
%o A028324 A028324:= func< n,k | Binomial(n+3, k+2+Floor((n+1)/2)) + 3*Binomial(n+1, k+1+Floor((n+1)/2)) >;
%o A028324 [A028324(n,k): k in [0..Floor(n/2)], n in [0..16]]; // _G. C. Greubel_, Jan 06 2024
%o A028324 (SageMath)
%o A028324 def A028324(n,k): return binomial(n+3, k+2+(n+1)//2) + 3*binomial(n+1, k+1+((n+1)//2))
%o A028324 flatten([[A028324(n,k) for k in range(1+(n//2))] for n in range(17)]) # _G. C. Greubel_, Jan 06 2024
%Y A028324 Cf. A028313, A028323.
%K A028324 nonn,tabf
%O A028324 0,1
%A A028324 _Mohammad K. Azarian_
%E A028324 More terms from _James Sellers_