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A177897
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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.
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3
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1, 255, 21845, 3342387, 286331153, 64424509455, 5519032976645, 844437815230467, 72340172838076673, 18446744073709551615, 1567973246265311887445, 241781474574111093044019
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OFFSET
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0,2
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COMMENTS
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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)].
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LINKS
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FORMULA
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MATHEMATICA
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a = Plus@@(x^Range[0, 7]); Table[FromDigits[Mod[CoefficientList[a^n, x], 2], 2], {n, 0, 15}]
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PROG
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(Python)
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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