

A235269


floor(s*t/(s+t)), where s(n) are the squares, t(n) the triangular numbers.


0



0, 1, 3, 6, 9, 13, 17, 23, 28, 35, 42, 50, 59, 68, 78, 88, 100, 111, 124, 137, 151, 166, 181, 197, 213, 231, 248, 267, 286, 306, 327, 348, 370, 392, 416, 439, 464, 489, 515, 542, 569, 597, 625, 655, 684, 715, 746, 778, 811, 844, 878, 912, 948, 983, 1020, 1057
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..56.
Index entries for linear recurrences with constant coefficients, signature (2,1,0,0,0,0,0,0,1,2,1).


FORMULA

a(n) = floor(s*t/(s+t)) where s = A000290(n) = n^2, t = A000217(n) = n*(n+1)/2. a(n) = floor((n^3+n^2) / (3*n+1)).
G.f.: (x^10 + 2*x^9  x^8 + 2*x^7 + x^5 + x^3 + x^2 + x)/((1x)^2*(1x^9)).  Ralf Stephan, Jan 15 2014


MATHEMATICA

With[{nn=60}, Floor[Times@@#/Total[#]]&/@Thread[{Range[nn]^2, Accumulate[ Range[ nn]]}]] (* or *) LinearRecurrence[{2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1}, {0, 1, 3, 6, 9, 13, 17, 23, 28, 35, 42}, 60] (* Harvey P. Dale, Oct 07 2015 *)


PROG

(Python)
for n in range(1, 99):
s = n*n
t = n*(n+1)/2
print str(s*t//(s+t))+', ',


CROSSREFS

Cf. A000217, A000290.
Sequence in context: A185173 A171662 A302292 * A004137 A080060 A004131
Adjacent sequences: A235266 A235267 A235268 * A235270 A235271 A235272


KEYWORD

nonn,easy


AUTHOR

Alex Ratushnyak, Jan 05 2014


STATUS

approved



