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A015219 Odd tetrahedral numbers: a(n) = (4*n+1)*(4*n+2)*(4*n+3)/6. 9

%I

%S 1,35,165,455,969,1771,2925,4495,6545,9139,12341,16215,20825,26235,

%T 32509,39711,47905,57155,67525,79079,91881,105995,121485,138415,

%U 156849,176851,198485,221815,246905,273819,302621,333375,366145,400995,437989

%N Odd tetrahedral numbers: a(n) = (4*n+1)*(4*n+2)*(4*n+3)/6.

%C Sum_{n>=0} 1/a(n) = (3/2)*log(2). [_Jaume Oliver Lafont_, Oct 20 2009]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

%F G.f.: (1+x)*(1+30*x+x^2)/(1-x)^4. [_Jaume Oliver Lafont_, Oct 20 2009]

%F From _Ant King_, Oct 19 2012: (Start)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F a(n) = 64 + 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

%F a(n) = A000292(4*n+1). - _L. Edson Jeffery_, Jan 16 2013

%F a(n) = A000447(2*n+1). - _Michel Marcus_, Jan 25 2016

%t LinearRecurrence[{4, -6, 4, -1}, {1, 35, 165, 455}, 35] (* _Ant King_, Oct 19 2012 *)

%t Table[(4 n + 1) (4 n + 2) (4 n + 3)/6, {n, 0, 40}] (* _Vincenzo Librandi_, Jan 25 2016 *)

%o (PARI) a(n)=binomial(4*n+3,3) \\ _Charles R Greathouse IV_, Jan 16 2013

%o (MAGMA) [(4*n+1)*(4*n+2)*(4*n+3)/6: n in [0..40]]; // _Vincenzo Librandi_, Jan 25 2016

%Y Cf. A000292.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_

%E More terms from _Erich Friedman_.

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Last modified January 18 19:43 EST 2020. Contains 331029 sequences. (Running on oeis4.)