A093361 Add/multiply sequence, see example.

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

Author

Jorge Coveiro, Apr 28 2004

Keywords

• nonn
• easy

Comments

It appears that a(2*n+1) = 2*(n + A002623(2*n-1)) + 3. - Carl Najafi, Jan 21 2013

Examples

			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
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Crossrefs

Cf. A002623.

Programs

Mathematica

LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,3,7,11,27,33,69},50] (* Harvey P. Dale, Jun 02 2019 *)

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

Extensions

More terms from Ralf Stephan, Dec 02 2004