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

0,2

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).

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]

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 *)

Prog

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

Crossrefs

Cf. A055249.

Sequence in context: A335470 A003262 A189162 * A117585 A317474 A279978

Adjacent sequences: A079279 A079280 A079281 * A079283 A079284 A079285

Keyword

easy,nonn

Author

Paul Barry, Feb 08 2003

Status

approved