A185096 Let T(n) = n(n+1)/2 be the n-th triangular number (A000217); a(n) = T(8T(n)).
0, 36, 300, 1176, 3240, 7260, 14196, 25200, 41616, 64980, 97020, 139656, 195000, 265356, 353220, 461280, 592416, 749700, 936396, 1155960, 1412040, 1708476, 2049300, 2438736, 2881200, 3381300, 3943836, 4573800, 5276376, 6056940, 6921060, 7874496, 8923200, 10073316, 11331180, 12703320, 14196456, 15817500, 17573556, 19471920, 21520080
Offset: 0
References
- C. Alsina and R. B. Nelson, Charming Proofs: A Journey into Elegant Mathematics, MAA, 2010. See p. 4.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Mathematica
Table[2*n*(n + 1)*(2*n + 1)^2, {n, 0, 50}] (* G. C. Greubel, Jun 22 2017 *) -
PARI
for(n=0,50, print1(2*n*(n+1)*(2*n+1)^2, ", ")) \\ G. C. Greubel, Jun 22 2017
Formula
From G. C. Greubel, Jun 22 2017: (Start)
a(n) = 2*n*(n + 1)*(2*n + 1)^2.
G.f.: 12*x*(3 + 10*x + 3*x^2)/(1 - x)^5.
E.g.f.: 2*x*(18 + 57*x + 32*x^2 + 4*x^3)*exp(x). (End)
Comments