A125200 a(n) = n*(4*n^2 + n - 1)/2.

2, 17, 57, 134, 260, 447, 707, 1052, 1494, 2045, 2717, 3522, 4472, 5579, 6855, 8312, 9962, 11817, 13889, 16190, 18732, 21527, 24587, 27924, 31550, 35477, 39717, 44282, 49184, 54435, 60047, 66032, 72402, 79169, 86345, 93942, 101972, 110447, 119379

Offset: 1

Author

Reinhard Zumkeller, Nov 24 2006

Keywords

• nonn
• easy

Comments

a(n) = Sum_{k=1..n} (4*n*k - n - k), sums of rows of the triangle in A125199.

A003415(A003415(a(n))) = 2*A016969(n-1).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Crossrefs

Cf. A003415, A016969, A033568, A125199.

Programs

Magma

[n*(4*n^2 +n-1)div 2:n in [1..40]]; // Vincenzo Librandi, Dec 27 2010

Mathematica

LinearRecurrence[{4,-6,4,-1},{2,17,57,134},40] (* Harvey P. Dale, Feb 05 2013 *)

Formula

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - R. J. Mathar, Feb 12 2010

G.f.: x*(2+9*x+x^2)/(x-1)^4. - R. J. Mathar, Feb 12 2010

a(n) = Sum_{i=1..n} A033568(i). - Bruno Berselli, Jul 22 2013

Extensions

Definition corrected by Vincenzo Librandi, Dec 27 2010