A154223 Diagonal sums of number triangle A154221.

1, 1, 2, 3, 5, 9, 16, 32, 61, 125, 246, 502, 999, 2023, 4040, 8136, 16265, 32649, 65290, 130826, 261643, 523787, 1047564, 2096140, 4192269, 8386573, 16773134, 33550350, 67100687, 134209551, 268419088, 536854544, 1073709073, 2147450897, 4294901778, 8589869074, 17179738131, 34359607315, 68719214612, 137438691348

Offset: 0

Author

Paul Barry, Jan 05 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,1,-9,4,6,-4).

Programs

Magma

I:=[1,1,2,3,5,9,16]; [n le 7 select I[n] else 3*Self(n-1)+Self(n-2)-9*Self(n-3)+4*Self(n-4)+6*Self(n-5)-4*Self(n-6): n in [1..40]]; // Vincenzo Librandi, Sep 07 2016

Maple

A154223 := proc(n)
    a := 0 ;
    for npr from n by -1 do
        k := n-npr ;
        if k <= npr then
            a := a+A154221(npr,k) ;
        else
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Feb 05 2015

Mathematica

Join[{1}, LinearRecurrence[{3, 1, -9, 4, 6, -4}, {1, 2, 3, 5, 9, 16}, 25]] (* G. C. Greubel, Sep 06 2016 *)

PARI

Vec((1-x-x^2)*(1-x-2*x^2+2*x^3-x^4)/((1-x)^2*(1+x)*(1-2*x)*(1-2*x^2)) + O(x^40)) \\ Colin Barker, Sep 07 2016

Formula

G.f.: (1 - x - x^2)*(1 - x - 2*x^2 + 2*x^3 - x^4) / ((1-x)^2*(1+x)*(1-2*x)*(1-2*x^2)). - Colin Barker, Sep 07 2016