A087462 -id:A087462 - cp's OEIS frontend

A087463 Generalized multiplicative Jacobsthal sequence.

0, 1, 1, 0, 5, 11, 0, 43, 85, 0, 341, 683, 0, 2731, 5461, 0, 21845, 43691, 0, 174763, 349525, 0, 1398101, 2796203, 0, 11184811, 22369621, 0, 89478485, 178956971, 0, 715827883, 1431655765, 0, 5726623061, 11453246123, 0, 45812984491, 91625968981, 0

Offset: 0

Paul Barry, Sep 08 2003

Set A001045(3n)=0 in A001045.

2^n = A087462(n) + a(n) + A087464(n) provides a decomposition of Pascal's triangle.

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).

concat(0, Vec(-x*(4*x^4-2*x^3+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

a(n) = Sum_{k=0..n} if (mod(n*k, 3)=1, 1, 0)*C(n, k).
a(n) = (2/9)*(1-cos(2*Pi*n/3))*(2^n-(-1)^n).
From Colin Barker, Nov 02 2015: (Start)
a(n) = 7*a(n-3)+8*a(n-6) for n>5.
G.f.: -x*(4*x^4-2*x^3+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
(End)

A087464 Generalized multiplicative Jacobsthal sequence.

Original entry on oeis.org

0, 0, 2, 0, 6, 10, 0, 42, 86, 0, 342, 682, 0, 2730, 5462, 0, 21846, 43690, 0, 174762, 349526, 0, 1398102, 2796202, 0, 11184810, 22369622, 0, 89478486, 178956970, 0, 715827882, 1431655766, 0, 5726623062, 11453246122, 0, 45812984490, 91625968982, 0

Offset: 0

Paul Barry, Sep 08 2003

2^n = A087462(n) + A087463(n) + a(n) provides a decomposition of Pascal's triangle.

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).

Cf. A001045, A087462, A087463.

LinearRecurrence[{0,0,7,0,0,8},{0,0,2,0,6,10},40] (* Harvey P. Dale, Aug 31 2015 *)

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

a(n) = Sum_{k=0..n} if(mod(n*k, 3)=2, 1, 0) * C(n, k).
a(n) = (2/9)*(2^n-3*0^n+2*(-1)^n)*(1-cos(2*Pi*n/3)).
From Colin Barker, Nov 02 2015: (Start)
a(n) = 7*a(n-3)+8*a(n-6) for n>5.
G.f.: 2*x^2*(2*x^3-3*x^2-1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
(End)

cp's OEIS Frontend

A087463 Generalized multiplicative Jacobsthal sequence.

Views

Author

Keywords

Comments

Links

Programs

PARI

Formula