A138190 Numerator of (n-1)*n*(n+1)/12.
0, 1, 2, 5, 10, 35, 28, 42, 60, 165, 110, 143, 182, 455, 280, 340, 408, 969, 570, 665, 770, 1771, 1012, 1150, 1300, 2925, 1638, 1827, 2030, 4495, 2480, 2728, 2992, 6545, 3570, 3885, 4218, 9139, 4940, 5330, 5740, 12341, 6622, 7095, 7590, 16215, 8648
Offset: 1
Examples
0, 1/2, 2, 5, 10, 35/2, 28, 42, 60, 165/2, 110, 143, 182, ...
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Eric Weisstein's World of Mathematics, Kirchhoff Index.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,4,0,0,0,-6,0,0,0,4,0,0,0,-1).
Programs
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Mathematica
Table[(n^3-n)/12,{n,50}]//Numerator (* or *) LinearRecurrence[{0,0,0,4,0,0,0,-6,0,0,0,4,0,0,0,-1},{0,1,2,5,10,35,28,42,60,165,110,143,182,455,280,340},50] (* Harvey P. Dale, Nov 05 2021 *) -
PARI
a(n) = numerator((n-1)*n*(n+1)/12); \\ Michel Marcus, Feb 17 2015
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PARI
a(n)=binomial(n+1,3)/if(n%4==2,1,2) \\ Charles R Greathouse IV, Feb 17 2015
Formula
a(n+2) = numerator of A000295(n+2)/(3*Integral_{t=0..2} t^n*(1-abs(1-t))^2).
a(n) = (n*(n-1)*(n+1)*(5+((-1)^n-(-1)^((2*n-1+(-1)^n)/4)-(-1)^((6*n-1+(-1)^n)/4))))/48. - Luce ETIENNE, Feb 17 2015
G.f.: x^2*(x^12 +2*x^11 +5*x^10 +10*x^9 +31*x^8 +20*x^7 +22*x^6 +20*x^5 +31*x^4 +10*x^3 +5*x^2 +2*x +1) / ((x -1)^4*(x +1)^4*(x^2 +1)^4). - Colin Barker, Feb 17 2015
Sum_{n>=2} 1/a(n) = 3 * (1 - log(2)/2). - Amiram Eldar, Aug 11 2022