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

1,3

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).

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

Example

0, 1/2, 2, 5, 10, 35/2, 28, 42, 60, 165/2, 110, 143, 182, ...

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 *)

Prog

(PARI) a(n) = numerator((n-1)*n*(n+1)/12); \\ Michel Marcus, Feb 17 2015
(PARI) a(n)=binomial(n+1, 3)/if(n%4==2, 1, 2) \\ Charles R Greathouse IV, Feb 17 2015

Crossrefs

Cf. A000295, A138191.

Sequence in context: A270521 A089073 A343167 * A056300 A326006 A144636

Adjacent sequences: A138187 A138188 A138189 * A138191 A138192 A138193

Keyword

nonn,frac,easy

Author

Eric W. Weisstein, Mar 04 2008

Status

approved