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A154223 Diagonal sums of number triangle A154221. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A047061 A136169 A047041 * A061031 A326023 A326117

Adjacent sequences:  A154220 A154221 A154222 * A154224 A154225 A154226

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jan 05 2009

STATUS

approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)