

A195038


41 times triangular numbers.


1



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
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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 / (x1)^3 .  R. J. Mathar, Oct 04 2014


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



