login
A093361
Add/multiply sequence, see example.
15
1, 3, 7, 11, 27, 33, 69, 77, 141, 151, 251, 263, 407, 421, 617, 633, 889, 907, 1231, 1251, 1651, 1673, 2157, 2181, 2757, 2783, 3459, 3487, 4271, 4301, 5201, 5233, 6257, 6291, 7447, 7483, 8779, 8817, 10261, 10301, 11901, 11943, 13707, 13751, 15687, 15733, 17849
OFFSET
0,2
COMMENTS
It appears that a(2*n+1) = 2*(n + A002623(2*n-1)) + 3. - Carl Najafi, Jan 21 2013
FORMULA
a(n) = (1/24)*(4*n^3 + 12*n^2 + 20*n + 33 + (6*n^2 - 9)*(-1)^n). - Ralf Stephan, Dec 02 2004
G.f.: (1 + 2*x + x^2 - 2*x^3 + 7*x^4 - x^6)/((1 + x)^3*(x - 1)^4). - R. J. Mathar, May 20 2013
E.g.f.: ((12 + 15*x + 15*x^2 + 2*x^3)*cosh(x) + (21 + 21*x + 9*x^2 + 2*x^3)*sinh(x))/12. - Stefano Spezia, Apr 18 2023
EXAMPLE
a(0) = 1
a(1) = 1+2
a(2) = 1+2*3
a(3) = 1+2*3+4
a(4) = 1+2*3+4*5
a(5) = 1+2*3+4*5+6
a(6) = 1+2*3+4*5+6*7
a(7) = 1+2*3+4*5+6*7+8
a(8) = 1+2*3+4*5+6*7+8*9
MATHEMATICA
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 3, 7, 11, 27, 33, 69}, 50] (* Harvey P. Dale, Jun 02 2019 *)
CROSSREFS
Cf. A002623.
Sequence in context: A024459 A001645 A103798 * A227364 A051202 A211674
KEYWORD
nonn,easy
AUTHOR
Jorge Coveiro, Apr 28 2004
EXTENSIONS
More terms from Ralf Stephan, Dec 02 2004
STATUS
approved