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A028315 Odd elements in the 5-Pascal triangle A028313.

%I A028315 #20 Jul 02 2025 16:01:56
%S A028315 1,1,1,1,5,1,1,1,1,7,7,1,1,19,19,1,1,9,27,27,9,1,1,65,65,1,1,11,101,
%T A028315 101,11,1,1,57,147,231,231,147,57,1,1,13,69,69,13,1,1,273,273,1,1,15,
%U A028315 355,855,855,355,15,1,1,111,451,2277,2277,451,111,1,1,17,127,1661,3487,5379,5379,3487,1661,127,17,1
%N A028315 Odd elements in the 5-Pascal triangle A028313.
%H A028315 G. C. Greubel, <a href="/A028315/b028315.txt">Table of n, a(n) for n = 0..1000</a>
%e A028315 Odd elements of A028313 as an irregular triangle:
%e A028315   1;
%e A028315   1,   1;
%e A028315   1,   5,   1;
%e A028315   1,   1;
%e A028315   1,   7,   7,   1;
%e A028315   1,  19,  19,   1;
%e A028315   1,   9,  27,  27,   9,   1;
%e A028315   1,  65,  65,   1;
%e A028315   1,  11, 101, 101,  11,   1;
%e A028315   1,  57, 147, 231, 231, 147, 57, 1;
%e A028315   1,  13,  69,  69,  13,   1;
%e A028315   1, 273, 273,   1;
%e A028315   1,  15, 355, 855, 855, 355, 15, 1;
%e A028315   ...
%t A028315 A028313[n_, k_]:= If[n<2, 1, Binomial[n,k] +3*Binomial[n-2,k-1]];
%t A028315 f= Table[A028313[n, k], {n,0,100}, {k,0,n}]//Flatten;
%t A028315 a[n_]:= DeleteCases[{f[[n+1]]}, _?EvenQ];
%t A028315 Table[a[n], {n,0,150}]//Flatten (* _G. C. Greubel_, Jan 06 2024 *)
%o A028315 (Magma)
%o A028315 A028313:= func< n, k | n le 1 select 1 else Binomial(n, k) +3*Binomial(n-2, k-1) >;
%o A028315 a:=[A028313(n, k): k in [0..n], n in [0..100]];
%o A028315 [a[n]: n in [1..150] | (a[n] mod 2) eq 1]; // _G. C. Greubel_, Jan 06 2024
%o A028315 (SageMath)
%o A028315 def A028313(n, k): return 1 if n<2 else binomial(n, k) + 3*binomial(n-2, k-1)
%o A028315 a=flatten([[A028313(n, k) for k in range(n+1)] for n in range(101)])
%o A028315 [a[n] for n in (0..150) if a[n]%2==1] # _G. C. Greubel_, Jan 06 2024
%Y A028315 Cf. A028313, A028316, A028325.
%K A028315 nonn,tabf
%O A028315 0,5
%A A028315 _Mohammad K. Azarian_
%E A028315 More terms from _James Sellers_