A087462 - OEIS

A087462

Generalized mod 3 multiplicative Jacobsthal sequence.

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

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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: A380601 A198996 A316689 * A168204 A193681 A347902

Adjacent sequences: A087459 A087460 A087461 * A087463 A087464 A087465

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 08 2003

STATUS

approved