A085740 a(n) = T(n)^2 - n^2, where T(n) is a triangular number.
0, 0, 5, 27, 84, 200, 405, 735, 1232, 1944, 2925, 4235, 5940, 8112, 10829, 14175, 18240, 23120, 28917, 35739, 43700, 52920, 63525, 75647, 89424, 105000, 122525, 142155, 164052, 188384, 215325, 245055, 277760, 313632, 352869, 395675, 442260
Offset: 0
Examples
a(3) = T(3)^2 - 3^2 = 6^2 - 9 = 36-9 = 27.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- M. Sitaramayya, Curvature tensors in Kaehler manifolds, Transactions of the AMS, 183 (September 1973), 341-353.
- Eric Weisstein's World of Mathematics, Harary Index
- Eric Weisstein's World of Mathematics, Rook Graph
- Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
Programs
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Magma
[n^2*(n^2+2*n-3)/4: n in [0..40]]; // Vincenzo Librandi, Sep 09 2011
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Mathematica
Table[(n - 1) n^2 (n + 3)/4, {n, 20}] (* Eric W. Weisstein, Jun 20 2017 *) Table[PolygonalNumber[n]^2 - n^2, {n, 20}] (* Eric W. Weisstein, Jun 20 2017 *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 5, 27, 84, 200}, 20] (* Eric W. Weisstein, Jun 20 2017 *) CoefficientList[Series[(x (-5 - 2 x + x^2))/(-1 + x)^5, {x, 0, 20}], x] (* Eric W. Weisstein, Jun 20 2017 *) -
PARI
for(n=0,50,print1(n^2*(n^2-9)/4","))
Formula
a(n) = n^2*(n^2+2*n-3)/4.
a(n) = 4*A173963(n+1). - Reinhard Zumkeller, Mar 03 2010
G.f.: x^2*(5+2*x-x^2)/(1-x)^5. - Colin Barker, Mar 17 2012
Comments