A158561 a(n) = ((2^n)*((2^n)+1) - (2^(n-1))*((2^(n-1))+1))/2, a(1)=3.

3, 7, 26, 100, 392, 1552, 6176, 24640, 98432, 393472, 1573376, 6292480, 25167872, 100667392, 402661376, 1610629120, 6442483712, 25769869312, 103079346176, 412317122560, 1649267965952, 6597070815232, 26388281163776, 105553120460800, 422212473454592

Offset: 1

Author

Ctibor O. Zizka, Mar 21 2009

Keywords

• easy
• nonn

Comments

a(n) gives the number of elements with the length of n-digits, base B, in the addition matrix <0;B^n -1> x <0;B^n -1>. a(1)=B*(B+1)/2. a(n)=((B^n)*((B^n)+1) - (B^(n-1))*((B^(n-1))+1))/2.

Essentially the same as A049775. [R. J. Mathar, Mar 26 2009]

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-8)

Crossrefs

Cf. A000217

Cf. A006516. [Jaume Oliver Lafont, Mar 27 2009]

Programs

Mathematica

LinearRecurrence[{6,-8},{3,7,26},30] (* Harvey P. Dale, Feb 25 2017 *)

Formula

G.f.: x*(1-x)*(3-8*x)/((1-2*x)*(1-4*x)). [Jaume Oliver Lafont, Mar 27 2009]

G.f.: (3-11*x+8*x^2)/(1-6*x+8*x^2). - Harvey P. Dale, Feb 25 2017

Extensions

More terms from Harvey P. Dale, Feb 25 2017