A154292 Integers of the form m*(6*m -+ 1)/2.

11, 13, 46, 50, 105, 111, 188, 196, 295, 305, 426, 438, 581, 595, 760, 776, 963, 981, 1190, 1210, 1441, 1463, 1716, 1740, 2015, 2041, 2338, 2366, 2685, 2715, 3056, 3088, 3451, 3485, 3870, 3906, 4313, 4351, 4780, 4820, 5271, 5313, 5786, 5830, 6325, 6371

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

From Colin Barker, Feb 26 2016: (Start)

a(n) = (12*n^2 - 10*(-1)^n*n + 12*n - 5*(-1)^n + 5)/4.

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5.

G.f.: x*(11 + 2*x + 11*x^2) / ((1-x)^3*(1+x)^2). (End)

E.g.f.: (1/4)*(-5 + 10*x + (5 + 24*x + 12*x^2)*exp(2*x))*exp(-x). - G. C. Greubel, Sep 10 2016

From Amiram Eldar, Mar 18 2022: (Start)

Sum_{n>=1} 1/a(n) = 131/11 - (2+sqrt(3))*Pi.

Sum_{n>=1} (-1)^(n+1)/a(n) = 133/11 - 3*log(12) - 2*sqrt(3)*log(2+sqrt(3)). (End)

Mathematica

Flatten[Table[{n (6n-1)/2, n (6n+1)/2}, {n, 2, 50, 2}]] (* Harvey P. Dale, Jan 19 2013 *)

Prog

(PARI) Vec(x*(11+2*x+11*x^2)/((1-x)^3*(1+x)^2) + O(x^60)) \\ Colin Barker, Feb 26 2016
(Magma) &cat[[n*(6*n-1) div 2, n*(6*n+1) div 2]: n in [2..60 by 2]]; // Vincenzo Librandi, Sep 10 2016

Crossrefs

Cf. A001318, A074378, A057569, A057570.

Sequence in context: A045467 A108264 A023268 * A188386 A027450 A234799

Adjacent sequences: A154289 A154290 A154291 * A154293 A154294 A154295

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Status

approved