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A079825 Sum of numbers in n-th upward diagonal of triangle in A079826. 2
1, 3, 6, 15, 26, 41, 62, 92, 129, 169, 224, 287, 366, 443, 548, 656, 793, 919, 1090, 1255, 1466, 1653, 1906, 2140, 2441, 2701, 3052, 3367, 3774, 4119, 4584, 4992, 5521, 5963, 6558 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,2,-2,-2,2,-1,1,1,-1).

FORMULA

G.f. x*( 1+2*x+2*x^2+7*x^3+6*x^4+6*x^6+x^7+2*x^5+x^8 ) / ( (x^2+1)^2*(1+x)^3*(x-1)^4 ). - R. J. Mathar, Sep 05 2012

a(n) = ( (2*n+1)*(7*n^2+7*n+12) -3*n*(n-7)*(-1)^n +6*(2*n-3*(-1)^n+1)*i^(n*(n-1)) )/96, where i=sqrt(-1). - Bruno Berselli, Sep 05 2012

MAPLE

A079825 := proc(n)

        local a, k;

        a := 0 ;

        for k from 1 to (n+1)/2 do

                a := a+A056011(n-k+1, k) ;

        end do:

        a ;

end proc: # R. J. Mathar, Sep 05 2012

MATHEMATICA

LinearRecurrence[{1, 1, -1, 2, -2, -2, 2, -1, 1, 1, -1}, {1, 3, 6, 15, 26, 41, 62, 92, 129, 169, 224}, 35] (* Bruno Berselli, Sep 05 2012 *)

PROG

(MAGMA) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x+2*x^2+7*x^3+6*x^4+6*x^6+x^7+2*x^5+x^8)/((x^2+1)^2*(1+x)^3*(x-1)^4))); // Bruno Berselli, Sep 05 2012

(Maxima) makelist(expand(((2*n+1)*(7*n^2+7*n+12)-3*n*(n-7)*(-1)^n+6*(2*n-3*(-1)^n+1)*%i^(n*(n-1)))/96), n, 1, 35); [Bruno Berselli, Sep 05 2012]

CROSSREFS

Cf. A079826, A056011.

Sequence in context: A284168 A216304 A020991 * A327067 A252745 A282662

Adjacent sequences:  A079822 A079823 A079824 * A079826 A079827 A079828

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Feb 11 2003

STATUS

approved

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Last modified November 21 14:56 EST 2019. Contains 329371 sequences. (Running on oeis4.)