A049779 a(n) = Sum_{k=1..floor(n/2)} T(n, 2k), array T as in A049777.
2, 5, 13, 23, 41, 62, 94, 130, 180, 235, 307, 385, 483, 588, 716, 852, 1014, 1185, 1385, 1595, 1837, 2090, 2378, 2678, 3016, 3367, 3759, 4165, 4615, 5080, 5592, 6120, 6698, 7293, 7941, 8607, 9329, 10070, 10870, 11690, 12572, 13475, 14443, 15433
Offset: 2
Links
- Vincenzo Librandi, Table of n, a(n) for n = 2..1000
- M. Benoumhani and M. Kolli, Finite topologies and partitions, JIS 13 (2010) # 10.3.5, Lemma 6 2nd line.
- Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
Programs
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GAP
List([2..50], n-> (8*n^3 +6*n^2 -2*n -3 +3*(-1)^n*(2*n+1))/48); # G. C. Greubel, Dec 12 2019
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MATLAB
a = @(n) 1/4*(n*(n+1)*(4*n-1)/6 + (-1)^n*floor((n+1)/2)); % Néstor Jofré, Apr 24 2017
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Magma
[n^3/6+n^2/8-n/24-1/16+(-1)^n*(n/8+1/16): n in [2..50]]; // Vincenzo Librandi, Apr 25 2017
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Maple
seq( (8*n^3 +6*n^2 -2*n -3 +3*(-1)^n*(2*n+1))/48, n=2..50); # G. C. Greubel, Dec 12 2019
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Mathematica
T[m_, n_]:=(m+n)(m-n+1)/2; Table[Sum[T[n, 2k], {k, Floor[n/2]}], {n, 2, 50}] (* Indranil Ghosh, Apr 24 2017 *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {2, 5, 13, 23, 41, 62}, 50] (* Vincenzo Librandi, Apr 25 2017 *) -
PARI
a(n)=(4*n^3 + 3*n^2 + 2*n - if(n%2,6*n+3))/24 \\ Charles R Greathouse IV, Jun 08 2015
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Sage
[(8*n^3 +6*n^2 -2*n -3 +3*(-1)^n*(2*n+1))/48 for n in (2..50)] # G. C. Greubel, Dec 12 2019
Formula
G.f.: x^2*(2+x+x^2)/((1-x)^4*(1+x)^2). Pairwise sums of A023856. - Ralf Stephan, May 06 2004
a(n) = Sum_{k=1..n} k*floor(k/2). - Vladeta Jovovic, Apr 29 2006
a(n) = (8*n^3 + 6*n^2 - 2*n - 3 + 3*(-1)^n *(2*n+1))/48. - Robert Israel, Jun 08 2015
a(n) = (n*(n+1)*(4*n-1) + 6*(-1)^n*floor((n+1)/2))/24. - Néstor Jofré, Apr 24 2017
E.g.f.: ( (8*x^3 + 30*x^2 + 12*x - 3)*exp(x) + 3*(1-2*x)*exp(-x) )/48. - G. C. Greubel, Dec 12 2019
Extensions
More terms from Ralf Stephan, May 06 2004
Comments