A079282 Diagonal sums of triangle A055249.

1, 3, 9, 24, 61, 149, 354, 823, 1881, 4240, 9449, 20857, 45666, 99291, 214589, 461336, 987221, 2103917, 4467394, 9454895, 19951601, 41989408, 88155409, 184670769, 386072386, 805624179, 1678235829, 3490492968, 7249103581, 15034563845

Offset: 0

Author

Paul Barry, Feb 08 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-7,0,4).

Crossrefs

Cf. A055249.

Programs

Magma

[(n-1)*2^n + Fibonacci(n+3): n in [0..30]]; // Vincenzo Librandi, Aug 05 2013

Mathematica

Table[(n - 1) 2^n + Fibonacci[n + 3], {n, 0, 30}] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{5,-7,0,4},{1,3,9,24},30] (* Harvey P. Dale, May 29 2021 *)

Formula

a(n) = sum(sum((k+1)binomial(n-j, n-2j-k), k, 0, n-2j), j, 0, floor(n/2))

a(n) = (n-1)*2^n + F(n+3), with F(n) = A000045(n). - Ralf Stephan, May 09 2004

G.f.: (1-x)^2 / ((1-2*x)^2 * (1-x-x^2)). [Joerg Arndt, Aug 05 2013]