

A177897


Triangle of octanomial coefficients read by rows: nth row is obtained by expanding ((1+x)*(1+x^2)*(1+x^4))^n ] mod 2 and converting to decimal.


2



1, 255, 21845, 3342387, 286331153, 64424509455, 5519032976645, 844437815230467, 72340172838076673, 18446744073709551615, 1567973246265311887445, 241781474574111093044019
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OFFSET

0,2


COMMENTS

A generalization: Denote {a_k(n)}_(n>=0) the sequence of triangle of 2^knomial coefficients [read by rows: nth row is obtained by expanding ((1+x)*(1+x^2)*...*(1+x^(2^(k1)))^n ] mod 2 converted to decimal. Then a_k(n)=A001317((2^k1)*n). [Proof is based on the fact (following from the Lucas theorem for the binomial coefficients) that the kth row of Pascal triangle contains odd coefficients only iff k is Mersenne number (k=2^m1)].


LINKS

Table of n, a(n) for n=0..11.


FORMULA

a(n)=A001317(7*n).


MATHEMATICA

a = Plus@@(x^Range[0, 7]); Table[FromDigits[Mod[CoefficientList[a^n, x], 2], 2], {n, 0, 15}]


CROSSREFS

A001317 A177882
Sequence in context: A321553 A321547 A221970 * A160913 A022190 A267545
Adjacent sequences: A177894 A177895 A177896 * A177898 A177899 A177900


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Dec 15 2010


STATUS

approved



