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A087462 Generalized mod 3 multiplicative Jacobsthal sequence. 3
1, 1, 1, 8, 5, 11, 64, 43, 85, 512, 341, 683, 4096, 2731, 5461, 32768, 21845, 43691, 262144, 174763, 349525, 2097152, 1398101, 2796203, 16777216, 11184811, 22369621, 134217728, 89478485, 178956971, 1073741824, 715827883, 1431655765, 8589934592, 5726623061 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

2^n = a(n) + A087463(n) + A087464(n) provides a decomposition of Pascal's triangle.

Multiplicative analog of A078008.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,7,0,0,8).

FORMULA

a(n) = Sum_{k=0..n} if (mod(n*k, 3)=0, 1, 0) * C(n, k).

a(n) = 2^n-2/3*(1-cos(2*Pi*n/3))*(A001045(n)+2*A001045(n-1)+0^n).

From Colin Barker, Nov 02 2015: (Start)

a(n) = 7*a(n-3)+8*a(n-6) for n>5.

G.f.: -(4*x^5-2*x^4+x^3+x^2+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).

(End)

PROG

(PARI) Vec(-(4*x^5-2*x^4+x^3+x^2+x+1)/((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)) + O(x^100)) \\ Colin Barker, Nov 02 2015

CROSSREFS

Cf. A001045, A001018 (trisection), A082311 (trisection), A082365 (trisection).

Sequence in context: A154210 A198996 A316689 * A168204 A193681 A253806

Adjacent sequences:  A087459 A087460 A087461 * A087463 A087464 A087465

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 08 2003

STATUS

approved

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Last modified February 18 09:39 EST 2020. Contains 332011 sequences. (Running on oeis4.)