A087464 -id:A087464 - cp's OEIS frontend

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

Offset: 0

Paul Barry, Sep 08 2003

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

Multiplicative analog of A078008.

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

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

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)

A087463 Generalized multiplicative Jacobsthal sequence.

Original entry on oeis.org

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)

cp's OEIS Frontend

A087462 Generalized mod 3 multiplicative Jacobsthal sequence.

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