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A195039 23 times triangular numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
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.
Sequence in context: A078622 A280376 A134428 * A042036 A042034 A042038
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 12 2011
STATUS
approved

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Last modified June 23 03:01 EDT 2024. Contains 373629 sequences. (Running on oeis4.)