A195038 41 times triangular numbers.

0, 41, 123, 246, 410, 615, 861, 1148, 1476, 1845, 2255, 2706, 3198, 3731, 4305, 4920, 5576, 6273, 7011, 7790, 8610, 9471, 10373, 11316, 12300, 13325, 14391, 15498, 16646, 17835, 19065, 20336, 21648, 23001, 24395, 25830, 27306, 28823, 30381, 31980

Offset: 0

Author

Omar E. Pol, Sep 12 2011

Keywords

• nonn
• easy

Comments

Related to the primitive Pythagorean triple [21, 20, 29].

Sequence found by reading the line from 0, in the direction 0, 41, ..., and the same line from 0, in the direction 0, 123, ..., in the Pythagorean spiral whose edges have length A195033 and whose vertices are the numbers A195034. This is the main diagonal of the square spiral.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Bisection of A195034.

Cf. A000217, A195033.

Programs

Mathematica

41*Accumulate[Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,41,123},40] (* Harvey P. Dale, Nov 20 2015 *)

PARI

a(n)=41*n*(n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = (41*n^2 + 41*n)/2 = 41*n*(n+1)/2 = 41*A000217(n).

G.f.: -41*x/(x-1)^3. - R. J. Mathar, Oct 04 2014

From Elmo R. Oliveira, Dec 27 2024: (Start)

E.g.f.: 41*exp(x)*x*(2 + x)/2.

a(n) = A195034(2*n).

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