cp's OEIS Frontend

A027008 a(n) = greatest number in row n of array T given by A026998.

%I A027008 #10 Jul 24 2025 05:52:44
%S A027008 1,1,4,8,13,26,54,101,174,370,743,1397,2552,5353,10636,20120,38138,
%T A027008 78753,155793,296248,573382,1173183,2316317,4423690,8673078,17641499,
%U A027008 34801731,66705394,131894869,267203186,526966454,1013155981
%N A027008 a(n) = greatest number in row n of array T given by A026998.
%H A027008 G. C. Greubel, <a href="/A027008/b027008.txt">Table of n, a(n) for n = 0..1000</a>
%t A027008 f[n_, k_]:= f[n, k]= Sum[Binomial[2*n-k+j,j]*LucasL[2*(k-n-j)], {j,0,k-n-1}];
%t A027008 A027960[n_, k_]:= LucasL[k+1] -f[n,k]*Boole[k>n];
%t A027008 b[n_]:= b[n]= Table[A027960[n,2*k], {k,0,n}];
%t A027008 A027008[n_]:= Max[b[n]];
%t A027008 Table[A027008[n], {n,0,50}] (* _G. C. Greubel_, Jul 24 2025 *)
%o A027008 (SageMath)
%o A027008 @CachedFunction
%o A027008 def t(n, k): # t = A027960
%o A027008     if (k>2*n): return 0
%o A027008     elif (k<n+1): return lucas_number2(k+1, 1, -1)
%o A027008     else: return t(n-1, k-2) + t(n-1, k-1)
%o A027008 def A026998(n, k): return t(n, 2*k)
%o A027008 def b(n): return flatten([A026998(n,k) for k in range(n+1)])
%o A027008 def A027008(n): return max(b(n))
%o A027008 print([A027008(n) for n in range(51)]) # _G. C. Greubel_, Jul 24 2025
%Y A027008 Cf. A026998.
%K A027008 nonn
%O A027008 0,3
%A A027008 _Clark Kimberling_
%E A027008 Offset changed by _G. C. Greubel_, Jul 24 2025