A005672 -id:A005672 - cp's OEIS frontend

A295735 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.

0, -1, 0, 1, 3, 8, 15, 31, 54, 101, 171, 304, 507, 875, 1446, 2449, 4023, 6728, 11007, 18247, 29766, 49037, 79827, 130912, 212787, 347795, 564678, 920665, 1493535, 2430584, 3940503, 6403855, 10377126, 16846517, 27289179, 44266768, 71687019, 116215931

Offset: 0

Clark Kimberling, Nov 30 2017

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-2).

Cf. A001622, A000045, A005672.

LinearRecurrence[{1, 3, -2, -2}, {0, -1, 0, 1}, 100]

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0; a(1) = -1, a(2) = 0, a(3) = 1.

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

A295736 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1.

Original entry on oeis.org

1, -2, -2, 1, -3, 8, 1, 29, 22, 91, 97, 268, 333, 761, 1030, 2111, 3013, 5764, 8521, 15565, 23574, 41699, 64249, 111068, 173269, 294577, 463750, 778807, 1234365, 2054132, 3272113, 5408165, 8647510, 14219515, 22801489, 37348684, 60019101, 98023145, 157780102

Offset: 0

Clark Kimberling, Nov 30 2017

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)

Cf. A001622, A000045, A005672.

LinearRecurrence[{1, 3, -2, -2}, {1, -2, -2, 1}, 100]

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1; a(1) = -2, a(2) = -2, a(3) = 1.

G.f.: (1 - 3 x - 3 x^2 + 11 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

A295737 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = -1, a(3) = 2.

Original entry on oeis.org

1, -1, -1, 2, -1, 9, 4, 29, 25, 86, 95, 245, 308, 681, 925, 1862, 2659, 5033, 7436, 13493, 20417, 35958, 55351, 95405, 148708, 252305, 396917, 665606, 1054331, 1752705, 2790652, 4608893, 7366777, 12106742, 19407983, 31776869, 51053780, 83354937, 134146573

Offset: 0

Clark Kimberling, Nov 30 2017

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)

Cf. A001622, A000045, A005672.

LinearRecurrence[{1, 3, -2, -2}, {1, -1, -1, 2}, 100]

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1; a(1) = -1, a(2) = -1, a(3) = 2.

G.f.: (1 - 2 x - 3 x^2 + 8 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

cp's OEIS Frontend

A295735 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A295736 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A295737 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = -1, a(3) = 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

cp's OEIS Frontend

A295735 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A295736 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A295737 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = -1, a(3) = 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A295735 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.

A295736 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1.

A295737 a(n) = a(n-1) + 3a(n-2) -2a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = -1, a(3) = 2.