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+2*x^5+6*x^6+x^7+x^8 ) / ( (1+x)^3*(1-x)^4*(1+x^2)^2 ). - 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
E.g.f.: (1/48)*( (6+24*x+30*x^2+7*x^3)*cosh(x) + (6+42*x+33*x^2+7*x^3)* sinh(x) + 6*(x-1)*cos(x) - 6*(x-2)*sin(x) ). - G. C. Greubel, Dec 10 2023
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+2*x^5+6*x^6+x^7+x^8)/((x^2+1)^2*(1+x)^3*(x-1)^4))); // Bruno Berselli, Sep 05 2012
(Magma) [((2*n+1)*(7*n^2+7*n+12) -3*(-1)^n*n*(n-7) +6*(-1)^Binomial(n, 2)*(2*n-3*(-1)^n+1))/96: n in [1..41]]; // G. C. Greubel, Dec 10 2023
(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 */
(SageMath) [((2*n+1)*(7*n^2+7*n+12)-3*(-1)^n*n*(n-7)+6*(-1)^binomial( n, 2)*(2*n-3*(-1)^n+1))/96 for n in range(1, 41)] # G. C. Greubel, Dec 10 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Feb 11 2003
STATUS
approved