A131780 Row sums of triangle A131779.

1, 4, 5, 10, 15, 26, 41, 68, 109, 178, 287, 466, 753, 1220, 1973, 3194, 5167, 8362, 13529, 21892, 35421, 57314, 92735, 150050, 242785, 392836, 635621, 1028458, 1664079, 2692538, 4356617, 7049156, 11405773, 18454930, 29860703, 48315634, 78176337, 126491972

Offset

1,2

Comments

a(n)/a(n-1) tends to phi; e.g., a(10)/a(9) = 178/109 = 1.633...

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1)

Formula

From Andrew Howroyd, Sep 01 2018: (Start)

a(n) = 2*Fibonacci(n+1) - (1 - (-1)^n)/2.

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n > 4.

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

(End)

Example

a(4) = 10 = sum of row 4 terms of triangle A131779: (3 + 1 + 5 + 1).

Mathematica

LinearRecurrence[{1, 2, -1, -1}, {1, 4, 5, 10}, 40] (* or *) CoefficientList[ Series[(1+3*x-x^2-2*x^3)/(1-x-2*x^2+x^3+x^4), {x, 0, 40}], x] (* Harvey P. Dale, Aug 27 2021 *)

Prog

(PARI) a(n) = 2*fibonacci(n+1) - (1 - (-1)^n)/2; \\ Andrew Howroyd, Sep 01 2018
(PARI) Vec((1 + 3*x - x^2 - 2*x^3)/((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^40)) \\ Andrew Howroyd, Sep 01 2018

Crossrefs

Row sums of A131779.

Sequence in context: A119040 A287578 A135104 * A354968 A102006 A118735

Adjacent sequences: A131777 A131778 A131779 * A131781 A131782 A131783

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 14 2007

Extensions

Terms a(11) and beyond from Andrew Howroyd, Sep 01 2018

Status

approved