A026999 Uniquification of A026998.

1, 4, 8, 11, 13, 19, 26, 29, 34, 43, 53, 54, 64, 73, 76, 89, 101, 103, 118, 134, 151, 169, 171, 174, 188, 196, 199, 208, 229, 251, 274, 281, 298, 323, 349, 370, 376, 404, 431, 433, 463, 487, 494, 518, 521, 526, 559, 593, 628, 634, 664, 701, 739, 743, 778, 818, 859, 901, 944, 988, 1033, 1079, 1126, 1148

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A026998, A027960.

Programs

Mathematica

f[n_, k_]:= f[n, k]= Sum[Binomial[2*n-k+j,j]*LucasL[2*(k-n-j)], {j,0,k-n-1}];
A027960[n_, k_]:= LucasL[k+1] -f[n,k]*Boole[k>n];
A026999= Table[A027960[n,2*k], {n,0,225}, {k,0,n}]//Flatten//Union;
Table[A026999[[n]], {n,120}] (* G. C. Greubel, Aug 21 2025 *)

SageMath

@CachedFunction
def t(n, k): # t = A027960
    if (k>2*n): return 0
    elif (kA026998(n, k): return t(n, 2*k)
A026999 = sorted(set( flatten([[A026998(n,k) for k in range(n+1)] for n in range(103)]) ))
print([A026999[n] for n in range(100)]) # G. C. Greubel, Aug 21 2025

Extensions

More terms added by G. C. Greubel, Aug 21 2025