A103177 a(n) = (7*3^n + 2n + 5)/4.

3, 7, 18, 50, 145, 429, 1280, 3832, 11487, 34451, 103342, 310014, 930029, 2790073, 8370204, 25110596, 75331771, 225995295, 677985866, 2033957578, 6101872713, 18305618117, 54916854328, 164750562960, 494251688855, 1482755066539

Offset: 0

Author

Creighton Dement, Mar 17 2005

Keywords

• nonn
• easy

Comments

A floretion-generated sequence relating sequences A007051 and A047926. (a(n)) results from a force transform of the sequence of powers of 3.

Floretion Algebra Multiplication Program, FAMP Code: 4jesleftforseq[A*B] with A = - .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e and B = + 'i + .5j' + .5k' + .5'ij' + .5'ik', 1vesforseq[A*B](n) = 3^(n+1), ForType: 1A.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A007051, A047926.

Programs

Mathematica

Table[(7*3^n+2*n+5)/4,{n,0,25}]  (* Harvey P. Dale, Feb 23 2011 *)

Formula

a(n) = 2*A007051(n) + A047926(n).

a(n) = 5*a(n-1)-7*a(n-2)+3*a(n-3). G.f.: (3-2*x)*(1-2*x)/((1-x)^2*(1-3*x)). [Colin Barker, Aug 28 2012]

Extensions

More terms from Harvey P. Dale, Feb 23 2011