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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. 2
1, 255, 21845, 3342387, 286331153, 64424509455, 5519032976645, 844437815230467, 72340172838076673, 18446744073709551615, 1567973246265311887445, 241781474574111093044019 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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)].

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

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Last modified October 14 12:31 EDT 2019. Contains 328006 sequences. (Running on oeis4.)