login
A180844
a(n) = (27^n - 2^n)/25.
6
0, 1, 29, 787, 21257, 573955, 15496817, 418414123, 11297181449, 305023899379, 8235645283745, 222362422662139, 6003785411879801, 162102206120758723, 4376759565260493713, 118172508262033346635, 3190657723074900391913
OFFSET
0,3
COMMENTS
The a(n+1) appear in several triangle sums of Nicomachus's table A036561, i.e., Ca2(3*n), Ca2(3*n+1)/3, Ca2(3*n+2)/9 and Ca3(n). See A180662 for information about these camel sums and other chess sums.
FORMULA
a(n) = (27^n - 2^n)/25.
G.f.: x/((27*x-1)*(2*x-1)).
MATHEMATICA
(#[[1]]-#[[2]])/25&/@Partition[Riffle[27^Range[0, 20], 2^Range[0, 20]], 2] (* Harvey P. Dale, Jan 22 2011 *)
PROG
(PARI) a(n) = (27^n - 2^n)/25 \\ Iain Fox, Dec 12 2017
(PARI) first(n) = Vec(x/((27*x-1)*(2*x-1)) + O(x^n), -n) \\ Iain Fox, Dec 12 2017
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Sep 21 2010
STATUS
approved