This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177897 #20 Oct 14 2024 02:53:21
%S A177897 1,255,21845,3342387,286331153,64424509455,5519032976645,
%T A177897 844437815230467,72340172838076673,18446744073709551615,
%U A177897 1567973246265311887445,241781474574111093044019,20552052528097949033496593,4660480146812799619066433295,396140812663555408357742346245,61084913312720243968763869790979
%N A177897 Triangle of octanomial coefficients read by rows: n-th row is obtained by expanding ((1+x)*(1+x^2)*(1+x^4))^n mod 2 and converting to decimal.
%C A177897 A generalization: Denote {a_k(n)}_(n>=0) the sequence of triangle of 2^k-nomial coefficients [read by rows: n-th row is obtained by expanding ((1+x)*(1+x^2)*...*(1+x^(2^(k-1)))^n ] mod 2 converted to decimal. Then a_k(n)=A001317((2^k-1)*n). [Proof is based on the fact (following from the Lucas theorem for the binomial coefficients) that the k-th row of Pascal triangle contains odd coefficients only iff k is Mersenne number (k=2^m-1)].
%F A177897 a(n) = A001317(7*n).
%t A177897 a = Plus@@(x^Range[0, 7]); Table[FromDigits[Mod[CoefficientList[a^n, x], 2], 2], {n, 0, 15}]
%o A177897 (Python)
%o A177897 def A177897(n): return sum((bool(~(m:=7*n)&m-k)^1)<<k for k in range(7*n+1)) # _Chai Wah Wu_, May 03 2023
%o A177897 (PARI) a(n) = subst(lift(Mod(1+'x, 2)^(7*n)), 'x, 2); \\ _Michel Marcus_, Oct 14 2024
%Y A177897 Cf. A001317, A008589, A177882.
%K A177897 nonn,easy
%O A177897 0,2
%A A177897 _Vladimir Shevelev_, Dec 15 2010
%E A177897 More terms from _Michel Marcus_, Oct 14 2024