OFFSET
0,2
COMMENTS
Also as a(n) = (1/6)*(9*n^3-3*n^2), n>0: structured pentagonal prism numbers (Cf. A100177 - structured prisms; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov 07 2004
Number of inequivalent tetrahedral edge colorings using at most n+1 colors so that no color appears only once. - David Nacin, Feb 22 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (1/2) *(3*n+2)*(n+1)^2.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=10, a(2)=36, a(3)=88. - Harvey P. Dale, Jun 26 2011
G.f.: (1+6*x+2*x^2)/(1-x)^4. - Colin Barker, Jun 08 2012
a(n) = Sum_{i=0..n} (n+1)*(3*i+1). - Bruno Berselli, Sep 08 2015
Sum_{n>=0} 1/a(n) = 9*log(3) - sqrt(3)*Pi - Pi^2/3 = 1.15624437161388... . - Vaclav Kotesovec, Oct 04 2016
EXAMPLE
* *
a(2) = * * + * * = 10.
* * * *
MATHEMATICA
Table[((1+n)^2*(2+3n))/2, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 10, 36, 88}, 40] (* Harvey P. Dale, Jun 26 2011 *)
PROG
(Magma) [(3*n+2)*(n+1)^2/2: n in [0..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) a(n)=(1/2)*(3*n+2)*(n+1)^2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 28 1999
STATUS
approved