A235269 floor(s*t/(s+t)), where s(n) are the squares, t(n) the triangular numbers.

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

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)/((1-x)^2*(1-x^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