cp's OEIS Frontend

A028316 Odd elements in the 5-Pascal triangle A028313 that are not 1.

%I A028316 #18 Jul 02 2025 16:01:56
%S A028316 5,7,7,19,19,9,27,27,9,65,65,11,101,101,11,57,147,231,231,147,57,13,
%T A028316 69,69,13,273,273,15,355,855,855,355,15,111,451,2277,2277,451,111,17,
%U A028316 127,1661,3487,5379,5379,3487,1661,127,17,689,2223,11583,11583,2223,689,19
%N A028316 Odd elements in the 5-Pascal triangle A028313 that are not 1.
%C A028316 Odd elements of A028314. - _G. C. Greubel_, Jan 06 2024
%H A028316 G. C. Greubel, <a href="/A028316/b028316.txt">Table of n, a(n) for n = 0..1000</a>
%e A028316 Odd elements of A028313 as an irregular triangle:
%e A028316    5;
%e A028316    7,   7;
%e A028316   19,  19;
%e A028316    9,  27,  27,   9;
%e A028316   65,  65;
%e A028316   11, 101, 101,  11;
%e A028316   57, 147, 231, 231, 147, 57;
%e A028316   ...
%t A028316 A028314[n_, k_]:= Binomial[n+2,k+1] +3*Binomial[n,k];
%t A028316 f= Table[A028314[n,k], {n,0,100}, {k,0,n}]//Flatten;
%t A028316 a[n_]:= DeleteCases[{f[[n+1]]}, _?EvenQ];
%t A028316 Table[a[n], {n,0,150}]//Flatten (* _G. C. Greubel_, Jan 06 2024 *)
%o A028316 (Magma)
%o A028316 A028314:= func< n, k | Binomial(n+2, k+1) + 3*Binomial(n, k) >;
%o A028316 a:=[A028314(n, k): k in [0..n], n in [0..100]];
%o A028316 [a[n]: n in [1..150] | (a[n] mod 2) eq 1]; // _G. C. Greubel_, Jan 06 2024
%o A028316 (SageMath)
%o A028316 def A028314(n, k): return binomial(n+2, k+1) + 3*binomial(n, k)
%o A028316 a=flatten([[A028314(n, k) for k in range(n+1)] for n in range(101)])
%o A028316 [a[n] for n in (0..150) if a[n]%2==1] # _G. C. Greubel_, Jan 06 2024
%Y A028316 Cf. A028313, A028314, A028315, A028325.
%K A028316 nonn,tabf,easy
%O A028316 0,1
%A A028316 _Mohammad K. Azarian_
%E A028316 More terms from _James Sellers_