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

0,2

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

Table of n, a(n) for n=0..39.

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

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)

Mathematica

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

Prog

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

Crossrefs

Bisection of A195034.

Cf. A000217, A195033.

Sequence in context: A135792 A256347 A232100 * A067896 A205797 A203804

Adjacent sequences: A195035 A195036 A195037 * A195039 A195040 A195041

Keyword

nonn,easy

Author

Omar E. Pol, Sep 12 2011

Status

approved