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%I #13 May 03 2023 14:35:20
%S 1,255,21845,3342387,286331153,64424509455,5519032976645,
%T 844437815230467,72340172838076673,18446744073709551615,
%U 1567973246265311887445,241781474574111093044019
%N 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 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 a(n)=A001317(7*n).
%t a = Plus@@(x^Range[0, 7]); Table[FromDigits[Mod[CoefficientList[a^n, x], 2], 2], {n, 0, 15}]
%o (Python)
%o 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
%Y A001317 A177882
%K nonn
%O 0,2
%A _Vladimir Shevelev_, Dec 15 2010
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