A132922 Row sums of triangle A132921.

1, 4, 10, 19, 32, 50, 75, 110, 160, 233, 342, 508, 765, 1168, 1806, 2823, 4452, 7070, 11287, 18090, 29076, 46829, 75530, 121944, 197017, 318460, 514930, 832795, 1347080, 2179178, 3525507, 5703878, 9228520, 14931473, 24159006, 39089428, 63247317, 102335560

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

Formula

Binomial transform of [1, 3, 3, 0, 1, -1, 2, -3, 5, -8, ...].

From Andrew Howroyd, Aug 28 2018: (Start)

a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n > 5.

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

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

(End)

Example

a(4) = 19 = sum of row 4 terms of triangle A132921: (4 + 4 + 5 + 6).
a(5) = 32 = (1, 4, 6, 4, 1) dot (1, 3, 3, 0, 1) = (1 + 12 + 18 + 0 + 1).

Mathematica

LinearRecurrence[{4, -5, 1, 2, -1}, {1, 4, 10, 19, 32}, 50] (* or *)
a[n_]:=n*(n - 1) + Fibonacci[n + 2] - 1; Array[a, 50] (* Stefano Spezia, Sep 01 2018 *)

Prog

(PARI) a(n) = n*(n-1) + fibonacci(n+2) - 1; \\ Andrew Howroyd, Aug 28 2018
(PARI) Vec((1 - x^2 - 2*x^3)/((1 - x)^3*(1 - x - x^2)) + O(x^40)) \\ Andrew Howroyd, Aug 28 2018

Crossrefs

Cf. A132922.

Sequence in context: A301256 A301092 A009868 * A307276 A008040 A009871

Adjacent sequences: A132919 A132920 A132921 * A132923 A132924 A132925

Keyword

nonn

Author

Gary W. Adamson, Sep 05 2007

Extensions

Terms a(11) and beyond from Andrew Howroyd, Aug 28 2018

Status

approved