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

Author

Gary W. Adamson, Sep 05 2007

Keywords

• nonn

Examples

			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).
		

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).

Crossrefs

Cf. A132922.

Programs

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 *)

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

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)

Extensions

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