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

0,2

Comments

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

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).

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

Adjacent sequences: A093358 A093359 A093360 * A093362 A093363 A093364

Keyword

nonn,easy

Author

Jorge Coveiro, Apr 28 2004

Extensions

More terms from Ralf Stephan, Dec 02 2004

Status

approved