A102301 a(n) = ((3*n + 1)*2^(n+3) + 9 + (-1)^n)/18.

1, 4, 13, 36, 93, 228, 541, 1252, 2845, 6372, 14109, 30948, 67357, 145636, 313117, 669924, 1427229, 3029220, 6407965, 13514980, 28428061, 59652324, 124897053, 260978916, 544327453, 1133394148, 2356266781, 4891490532, 10140895005, 20997617892, 43426891549

Offset: 0

Author

Creighton Dement, Feb 20 2005

Keywords

• easy
• nonn

Comments

A floretion-generated sequence resulting from particular transform of A000975.

Floretion Algebra Multiplication Program, FAMP Code: 2jesforseq[ + .5'i + 'kk' + .5'jk' ], 1vesforseq(n) = A000975(n+2)*(-1)^(n+1), ForType: 1A, LoopType: tes (2nd iteration)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• T. Etzion, On the stopping redundancy of Reed-Muller codes, IEEE Trans. Information Theory 52 (11) (2006) 4867-4879, also, arXiv:cs/0511056 [cs.IT], 2005.
• Toufik Mansour and Armend Sh. Shabani, Bargraphs in bargraphs, Turkish Journal of Mathematics (2018) Vol. 42, Issue 5, 2763-2773.
• Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,4).

Crossrefs

Cf. A000975, A000337, A045883, A001787, A059570, A137266, A008574, A059260.

Programs

Magma

[((3*n+1)*2^(n+3)+9+(-1)^n)/18: n in [0..40]]; // Vincenzo Librandi, Nov 21 2018

Mathematica

Table[((3n+1)*2^(n+3) + 9 + (-1)^n)/18, {n,0,50}] (* G. C. Greubel, Sep 27 2017 *)
LinearRecurrence[{4, -3, -4, 4}, {1, 4, 13, 36}, 50] (* Vincenzo Librandi, Nov 21 2018 *)

PARI

a(n)=((3*n+1)*2^(n+3)+9+(-1)^n)/18 \\ Charles R Greathouse IV, Oct 16 2015

Formula

G.f.: 1/((1-x^2)*(1-2*x)^2).

a(n+1) - 2*a(n) = A000975(n+2) (n-th number without consecutive equal binary digits)

a(n) + a(n+1) = A000337(n+2);

a(n+1) - a(n) = A045883(n+2);

a(n+2) - a(n) = A001787(n+3) ( Number of edges in n-dimensional hypercube );

a(n+2) - 2*a(n+1) + a(n) = A059570(n+3);

Convolution of "Number of fixed points in all 231-avoiding involutions in S_n" (A059570) with the natural numbers (A000027), treating the result as if offset=0. - Graeme McRae, Jul 12 2006

Equals triangle A059260 * A008574 as a vector, where A008574 = [1, 4, 8, 12, 16, 20, ...]. - Gary W. Adamson, Mar 06 2012