A195039 23 times triangular numbers.

0, 23, 69, 138, 230, 345, 483, 644, 828, 1035, 1265, 1518, 1794, 2093, 2415, 2760, 3128, 3519, 3933, 4370, 4830, 5313, 5819, 6348, 6900, 7475, 8073, 8694, 9338, 10005, 10695, 11408, 12144, 12903, 13685, 14490, 15318, 16169, 17043, 17940, 18860

Offset

0,2

Comments

Related to the primitive Pythagorean triple [15, 8, 17].

Sequence found by reading the line from 0, in the direction 0, 23, ..., and the same line from 0, in the direction 0, 69, ..., in the Pythagorean spiral whose edges have length A195035 and whose vertices are the numbers A195036. This is the main diagonal of the square spiral.

Links

Table of n, a(n) for n=0..40.

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

Formula

a(n) = (23*n^2 + 23*n)/2 = 23*n*(n+1)/2 = 23*A000217(n).

a(0)=0, a(1)=23, a(2)=69, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Aug 28 2012

From Elmo R. Oliveira, Dec 15 2024: (Start)

G.f.: 23*x/(1-x)^3.

E.g.f.: 23*exp(x)*x*(2 + x)/2.

a(n) = A069174(n+1) - 1. (End)

Mathematica

23*Accumulate[Range[0, 40]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 23, 69}, 50] (* Harvey P. Dale, Aug 28 2012 *)

Prog

(PARI) a(n)=23*n*(n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Bisection of A195036.

Cf. A000217, A069174, A195035.

Sequence in context: A078622 A280376 A134428 * A042036 A042034 A042038

Adjacent sequences: A195036 A195037 A195038 * A195040 A195041 A195042

Keyword

nonn,easy

Author

Omar E. Pol, Sep 12 2011

Status

approved