OFFSET
1,1
REFERENCES
H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 1974.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 16*n^3 - 15*n^2 + 6*n - 1.
G.f.: x*(6 + 55*x + 34*x^2 + x^3)/(1-x)^4. - Colin Barker, Feb 12 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=6, a(2)=79, a(3)=314, a(4)=807. - Harvey P. Dale, Aug 11 2015
MATHEMATICA
Table[16*n^3-15*n^2+6*n-1, {n, 1, 50}] (* Vincenzo Librandi, Feb 12 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {6, 79, 314, 807}, 50] (* Harvey P. Dale, Aug 11 2015 *)
PROG
(Magma) [16*n^3-15*n^2+6*n-1: n in [1..50]]; // Vincenzo Librandi, Feb 12 2012
(PARI) for(n=1, 40, print1(16*n^3-15*n^2+6*n-1", ")); \\ Vincenzo Librandi, Feb 12 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 08 2004
STATUS
approved