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

0,3

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).

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

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 *)

Prog

(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
(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

Crossrefs

Sequence in context: A136169 A047041 A352944 * A061031 A339512 A326023

Adjacent sequences: A154220 A154221 A154222 * A154224 A154225 A154226

Keyword

nonn,easy

Author

Paul Barry, Jan 05 2009

Status

approved