OFFSET
0,2
COMMENTS
Primes in sequence: 5, 92603307541, 52176309488123582020412161, ...
a(n) is divisible by n for n = 1, 2, 8, 55, 82, 171, 210, 1060, 1141, ...
LINKS
Bruno Berselli and G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 form Bruno Berselli)
FORMULA
Recurrence: 2*n*(2*n + 1)*a(n) = (31*n^2 + 2*n - 3)*a(n-1) - 3*(3*n - 1)*(3*n + 1)*a(n-2). - Vaclav Kotesovec, Oct 11 2015
a(n) ~ 27^(n + 3/2)/(23*sqrt(Pi*n)*4^(n + 1)). - Vaclav Kotesovec, Oct 11 2015
MATHEMATICA
Table[Sum[Binomial[3 k + 1, k], {k, 0, n}], {n, 0, 25}]
PROG
(Sage) [sum(binomial(3*k+1, k) for k in (0..n)) for n in (0..25)]
(Magma) [&+[Binomial(3*k+1, k): k in [0..n]]: n in [0..25]];
(Maxima) makelist(sum(binomial(3*k+1, k), k, 0, n), n, 0, 25);
(PARI) a(n) = sum(k=0, n, binomial(3*k+1, k)) \\ Colin Barker, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Oct 10 2015
STATUS
approved