A154327 Diagonal sums of number triangle A132046.

1, 1, 2, 5, 8, 15, 24, 41, 66, 109, 176, 287, 464, 753, 1218, 1973, 3192, 5167, 8360, 13529, 21890, 35421, 57312, 92735, 150048, 242785, 392834, 635621, 1028456, 1664079, 2692536, 4356617, 7049154, 11405773, 18454928, 29860703, 48315632, 78176337, 126491970, 204668309, 331160280, 535828591, 866988872

Offset: 0

Author

Paul Barry, Jan 07 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1).

Crossrefs

A shifted version of A066629.

Programs

Magma

[0^n-(3+(-1)^n)/2+2*Fibonacci(n+1):n in [0..40]]; // Vincenzo Librandi, Sep 12 2016

Mathematica

Join[{1}, LinearRecurrence[{1, 2, -1, -1}, {1, 2, 5, 8}, 25]] (* G. C. Greubel, Sep 11 2016 *)
CoefficientList[Series[(1 - x^2 + 2 x^3 + x^4) / ((1 - x^2) (1 - x - x^2)), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 12 2016 *)

Formula

G.f.: (1 - x^2 + 2x^3 + x^4)/( (1-x^2)*(1-x-x^2) ).

a(n) = 0^n - (3 + (-1)^n)/2 + 2*Fibonacci(n+1).