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A079825
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Sum of numbers in n-th upward diagonal of triangle in A079826.
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2
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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, 7071, 7738, 8289, 9030, 9660, 10481, 11153, 12056, 12815, 13806, 14611, 15692, 16592
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,1,-1,2,-2,-2,2,-1,1,1,-1).
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FORMULA
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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
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MAPLE
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local a, k;
a := 0 ;
for k from 1 to (n+1)/2 do
end do:
a ;
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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