login
A132925
a(n) = 2^n - 1 + n*(n-1)/2.
5
1, 4, 10, 21, 41, 78, 148, 283, 547, 1068, 2102, 4161, 8269, 16474, 32872, 65655, 131207, 262296, 524458, 1048765, 2097361, 4194534, 8388860, 16777491, 33554731, 67109188, 134218078, 268435833, 536871317, 1073742258, 2147484112
OFFSET
1,2
COMMENTS
Row sums of triangle A132924. n-th Mersenne number + (n-1)-th triangular number.
Partial sums of A006127. - Jaroslav Krizek, Oct 16 2009
FORMULA
Binomial transform of [1, 3, 3, 2, 2, 2, 2, ...].
a(n) = A000225(n) + A000217(n-1). - Jaroslav Krizek, Oct 16 2009
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(1)=1, a(2)=4, a(3)=10, a(4)=21. - Harvey P. Dale, Jun 19 2011
G.f.: -x*(x^2+x-1)/((x-1)^3*(2*x-1)). - Harvey P. Dale, Jun 19 2011
EXAMPLE
a(4) = 21 = sum of row 4 terms of triangle A132924: (4 + 4 + 5 + 8).
a(4) = 21 = (1, 3, 3, 1) dot (1, 3, 3, 2) = (1 + 9 + 9 + 2).
MAPLE
A132925 := proc(n) 2^n-1+n*(n-1)/2 ; end proc; # R. J. Mathar, Oct 23 2009
MATHEMATICA
Table[2^n-1+n (n-1)/2, {n, 40}] (* or *) LinearRecurrence[{5, -9, 7, -2}, {1, 4, 10, 21}, 40] (* Harvey P. Dale, Jun 19 2011 *)
PROG
(PARI) a(n)=2^n+binomial(n, 2)-1 \\ Charles R Greathouse IV, Jun 20 2011
(Magma) [2^n - 1 + n*(n-1)/2: n in [1..40]]; // Vincenzo Librandi, Jun 21 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Sep 05 2007
STATUS
approved