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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
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.
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
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.
Sequence in context: A135792 A256347 A232100 * A067896 A205797 A203804
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 12 2011
STATUS
approved